Peter Olver's Papers and Preprints

Last updated:   October 9, 2024

Note: The papers are listed in the order in which they were written, which is not necessarily the order in which they appear in print.

Moving Frames, Equivalence, and Pseudo-groups

  1. Olver, P.J., Using moving frames to construct equivariant maps, preprint, 2024.   pdf
  2. Olver, P.J., On the structure and generators of differential invariant algebras, in: Computer Algebra in Scientific Computing, F. Boulier, M. England, I. Kotsireas, T.M. Sadykov, E.V. Vorozhtsov, eds., Lecture Notes in Computer Science, vol. 14139, Springer-Verlag, New York, 2023, pp. 292-311.   pdf
  3. Olver, P.J., The outline signature of a convex body, preprint, 2022.   pdf
  4. Olver, P.J., Sabzevari, M., and Valiquette, F., Normal forms, moving frames, and differential invariants for nondegenerate hypersurfaces in C2, J. Geom. Anal. 33 (2023) 192.   pdf
  5. Olver, P.J., Projective invariants of images, European J. Appl. Math. 34 (2023) 936-946.   pdf
  6. Olver, P.J., A higher order moving frame for equi-affine plane curves, preprint, 2020.   pdf
  7. Olver, P.J., Qu, C., and Yang, Y., Feature matching and heat flow in centro-affine geometry, SIGMA: Symmetry Integrability Geom. Methods Appl. 16 (2020) 093.   pdf
  8. Olver, P.J., Invariants of finite and discrete group actions via moving frames, Bull. Iranian Math. Soc. 49 (2023) 11.   pdf
  9. Tuznik, S.L., Olver, P.J., and Tannenbaum, A., Equi-affine differential invariants for invariant feature point detection, European J. Appl. Math. 31 (2020) 277-296.   pdf
  10. Gün Polat, G., and Olver, P.J., Joint differential invariants of binary and ternary forms, Portugaliae Math. 76 (2019) 169-204.   Corrected version: pdf   Corrections and additions to published version: pdf
  11. Olver, P.J., Equivariant moving frames for Euclidean surfaces, preprint, 2016.   pdf
  12. Adams, S., and Olver, P.J., Prolonged analytic connected group actions are generically free, Transformation Groups 23 (2018), 893-913.   pdf
  13. Olver, P.J., Moving frame derivation of the fundamental equi-affine differential invariants for level set functions, preprint, 2015.   pdf
  14. Olver, P.J., The symmetry groupoid and weighted signature of a geometric object, J. Lie Theory 26 (2015), 235-267.   pdf
  15. Kogan, I.A., and Olver, P.J., Invariants of objects and their images under surjective maps, Lobachevskii J. Math. 36 (2015), 260-285.   Corrected version: pdf   Corrections and additions to published version: pdf
  16. Olver, P.J., and Valiquette, F., Recursive moving frames for Lie pseudo-groups, Results Math. 73 (2018), 57.   pdf
  17. Olver, P.J., Modern developments in the theory and applications of moving frames, London Math. Soc. Impact150 Stories 1 (2015), 14-50.   pdf
  18. Olver, P.J., Normal forms for submanifolds under group actions, in: Symmetries, Differential Equations and Applications, V. Kac, P.J. Olver, P. Winternitz, and T. Özer, eds., Proceedings in Mathematics & Statistics, Springer, New York, 2018, pp. 3-27.   pdf
  19. Olver, P.J., Recursive moving frames, Results Math. 60 (2011), 423-452.   Corrected version: pdf   Corrections to published version: pdf
  20. Olver, P.J., Recent advances in the theory and application of Lie pseudo-groups, in: XVIII International Fall Workshop on Geometry and Physics, M. Asorey, J.F. Cariñena, J. Clemente-Gallardo, and E. Martínez, AIP Conference Proceedings, vol. 1260, American Institute of Physics, Melville, NY, 2010, pp. 35-63.   pdf
  21. Olver, P.J., Differential invariant algebras, Contemp. Math. 549 (2011), 95-121.   pdf
  22. Olver, P.J., and Pohjanpelto, J., Persistence of freeness for pseudo-group actions, Arkiv Mat. 50 (2012), 165-182.   pdf
  23. Olver, P.J., Moving frames and differential invariants in centro-affine geometry, Lobachevskii J. Math. 31 (2010), 77-89.   pdf
  24. Itskov, V., Olver, P.J., and Valiquette, F., Lie completion of pseudo-groups, Transformation Groups 16 (2011), 161-173.   pdf
  25. Mari-Beffa, G., and Olver, P.J., Poisson structures for geometric curve flows on semi-simple homogeneous spaces, Regular and Chaotic Dynamics 15 (2010), 532-550.   pdf
  26. Olver, P.J., Pohjanpelto, J., and Valiquette, F., On the structure of Lie pseudo-groups, SIGMA: Symmetry Integrability Geom. Methods Appl. 5 (2009), 077.   pdf
  27. Olver, P.J., Lectures on moving frames, in: Symmetries and Integrability of Difference Equations, D. Levi, P. Olver, Z. Thomova, and P. Winternitz, eds., London Math. Soc. Lecture Note Series, vol. 381, Cambridge University Press, Cambridge, 2011, pp. 207-246.   pdf
  28. Olver, P.J., Differential invariants of maximally symmetric submanifolds, J. Lie Theory 19 (2009), 79-99.   Corrected version: pdf   Corrections to published version: pdf
  29. Olver, P.J., Invariant variational problems and invariant flows via moving frames, in: Variations, Geometry and Physics, O. Krupková, and D. Saunders, eds., Nova Science Publ., New York, 2009, pp. 209-235.   pdf
  30. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  31. Olver, P.J., and Pohjanpelto, J., Differential invariant algebras of Lie pseudo-groups, Adv. in Math. 222 (2009), 1746-1792.   Corrected version: pdf   Corrections to published version: pdf
  32. Hubert, E., and Olver, P.J., Differential invariants of conformal and projective surfaces, SIGMA: Symmetry Integrability Geom. Methods Appl. 3 (2007), 097.   pdf
  33. Olver, P.J., and Pohjanpelto, J., Moving frames and differential invariants for Lie pseudo-groups, in: Symmetry and Perturbation Theory, G. Gaeta, R. Vitolo, and S. Walcher, eds., World Scientific, Singapore, 2007, pp. 172-180.   pdf
  34. Kamran, N., Olver, P.J., and Tenenblat, K., Local symplectic invariants for curves, Commun. Contemp. Math. 11 (2009), 165-183.   pdf
  35. Olver, P.J., Differential invariants of surfaces, Diff. Geom. Appl. 27 (2009), 230-239.   pdf
  36. Olver, P.J., and Pohjanpelto, J., Differential invariants for Lie pseudo-groups, in: Gröbner Bases in Symbolic Analysis; M. Rosenkranz, D. Wang, eds, Radon Series Comp. Appl. Math., vol. 2, Walter de Gruyter, Berlin, 2007, pp. 217-243.   pdf
  37. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  38. Olver, P.J., and Pohjanpelto, J., Pseudo-groups, moving frames, and differential invariants, in: Symmetries and Overdetermined Systems of Partial Differential Equations, M. Eastwood and W. Miller, Jr., eds., IMA Volumes in Mathematics and Its Applications, vol. 144, Springer-Verlag, New York, 2008, pp. 127-149.   pdf
  39. Olver, P.J., Generating differential invariants, J. Math. Anal. Appl. 333 (2007), 450-471.   Corrected version: pdf   Corrections to published version: pdf
  40. Cheh, J., Olver, P.J., and Pohjanpelto, J., Algorithms for differential invariants of symmetry groups of differential equations, Found. Comput. Math. 8 (2008), 501-532.   pdf
  41. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  42. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004), 213-226.   pdf
  43. Olver, P.J., and Pohjanpelto, J., Regularity of pseudogroup orbits, in: Symmetry and Perturbation Theory, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, and S. Terracini, eds., World Scientific, Singapore, 2005, pp. 244-254.   pdf
  44. Cheh, J., Olver, P.J., and Pohjanpelto, J., Maurer-Cartan equations for Lie symmetry pseudo-groups of differential equations, J. Math. Phys., 46 (2005), 023504.   pdf
  45. Olver, P.J., An introduction to moving frames, in: Geometry, Integrability and Quantization; vol. 5, I.M. Mladenov, and A.C. Hirschfeld, eds., Softex, Sofia, Bulgaria, 2004, pp. 67-80.   pdf
  46. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005), 341-374.   pdf
  47. Olver, P.J., and Pohjanpelto, J., Moving frames for Lie pseudo-groups, Canadian J. Math. 60 (2008), 1336-1386.   pdf
  48. Olver, P.J., and Pohjanpelto, J., Maurer-Cartan forms and the structure of Lie pseudo-groups, Selecta Math. 11 (2005), 99-126.   pdf
  49. Olver, P.J., Moving frames, J. Symb. Comp. 36 (2003), 501-512.   pdf
  50. Olver, P.J., Moving frames: a brief survey, in: Symmetry and Perturbation Theory, D. Bambusi, M. Cadoni, and G. Gaeta, eds., World Scientific, Singapore, 2001, pp. 143-150.   pdf
  51. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001), 131-144.   Corrected version: pdf   Corrections to published version: pdf
  52. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003), 137-193.   Corrected version: pdf   Corrections to published version: pdf
  53. Olver, P.J., The canonical contact form, Adv. Studies Pure Math. 37 (2002), 267-285   pdf
  54. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  55. Olver, P.J., Moving frames, RIMS Kokyuroku 1150 (2000), 114-124.   pdf
  56. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   Updated version: pdf   Updates to published version: pdf
  57. Olver, P.J., Moving frames and joint differential invariants, Regular and Chaotic Dynamics 4 (4) (1999), 3-18.   pdf
  58. Olver, P.J., Joint invariant signatures, Found. Comput. Math. 1 (2001), 3-67.   pdf
  59. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000), 485-514.   pdf
  60. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999), 807-839.   pdf
  61. Olver, P.J., Moving frames and singularities of prolonged group actions, Selecta Math. 6 (2000), 41-77.   Corrected version: pdf   Corrections to published version: pdf
  62. Fels, M., and Olver, P.J., Moving frames and moving coframes, in: Algebraic Methods in Physics, Y. Saint-Aubin and L. Vinet, eds., CRM Series in Math. Phys., Springer-Verlag, New York, 2001, pp. 47-64.   pdf
  63. Fels, M., and Olver, P.J., Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999), 127-208.   Corrected version: pdf   Corrections to published version: pdf
  64. Fels, M., Olver, P.J., Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998), 161-213.   Corrected version: pdf   Corrections to published version: pdf
  65. Olver, P.J., Pseudo-stabilization of prolonged group actions. I. The order zero case, J. Nonlinear Math. Phys. 4 (1997), 271-277.   pdf
  66. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997), 701-732.   pdf
  67. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.   pdf
  68. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.   pdf
  69. Olver, P.J., Equivalence and the Cartan form, Acta Applicandae Math. 31 (1993), 99-136.   pdf
  70. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians III. New invariant differential equations, Nonlinearity 5 (1992), 601-621.   pdf
  71. Hsu, L., Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians II. The Cartan form for particle Lagrangians, J. Math. Phys. 30 (1989), 902-906.   pdf
  72. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians I. Formulation and reduction, J. Math. Pures et Appliquees 70 (1991), 369-391.   pdf
  73. Kamran, N., and Olver, P.J., Le probleme d'équivalence à une divergence près dans le calcul des variations des intégrales multiples, Comptes Rendus Acad. Sci. (Paris), Série I, 308 (1989), 249-252.   Scanned:  pdf
  74. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
  75. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.   pdf
  76. Kamran, N., and Olver, P.J., Equivalence problems for first order Lagrangians on the line, J. Diff. Eq. 80 (1989), 32-78.   pdf
  77. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.   pdf
  78. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.   pdf
  79. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.   pdf

Image Processing, Computer Vision, Anthropology

  1. O'Neill, R.C.W., Yezzi-Woodley, K., Calder, J., Olver, P.J., En masse scanning and automated surfacing of small objects using Micro-CT, preprint, 2024.   pdf
  2. Calder, J., Coil, R., Melton, J.A., Olver, P.J., Tostevin, G., and Yezzi-Woodley, K., Use and misuse of machine learning in anthropology, IEEE BITS 2 (1) (2022) 102-115.   pdf
  3. Yezzi-Woodley, K., Terwilliger, A., Li, J., Chen, E., Tappen, M., Calder, J., and Olver, P.J., Using machine learning on new feature sets extracted from three-dimensional models of broken animal bones to classify fragments according to break agent, J. Human Evolution, to appear.   pdf
  4. Yezzi-Woodley, K., Calder, J., Sweno, M., Siewert, C., and Olver, P.J., The Batch Artifact Scanning Protocol: A new method using computed tomography (CT) to rapidly create three-dimensional models of objects from large collections en masse, preprint, 2022.   pdf
  5. Olver, P.J., The outline signature of a convex body, preprint, 2022.   pdf
  6. Olver, P.J., Reconstruction of bodies from their projections, preprint, 2021.   pdf
  7. Yezzi-Woodley, K., Calder, J., Olver, P.J., Melton, J.A., Cody, P., Huffstutler, T., Terwilliger, A., Tappen, M., Coil, R., and Tostevin, G., The virtual goniometer: demonstrating a new method for measuring angles on archaeological materials using fragmentary bone, Archaeological Anthropological Sci. 13 (2021) 106.   pdf     Meshlab plugin
  8. Olver, P.J., Projective invariants of images, European J. Appl. Math. 34 (2023) 936-946.   pdf
  9. Olver, P.J., Qu, C., and Yang, Y., Feature matching and heat flow in centro-affine geometry, SIGMA: Symmetry Integrability Geom. Methods Appl. 16 (2020) 093.   pdf
  10. O'Neill, R.C.W., Angulo-Umaña, P., Calder, J., Hessburg, B., Olver, P.J., Shakiban, C., and Yezzi-Woodley, K., Computation of circular area and spherical volume invariants via boundary integrals, SIAM J. Imaging Sci. 13 (2020) 53-77.   pdf
  11. Tuznik, S.L., Olver, P.J., and Tannenbaum, A., Equi-affine differential invariants for invariant feature point detection, European J. Appl. Math. 31 (2020) 277-296.   pdf
  12. Olver, P.J., Moving frame derivation of the fundamental equi-affine differential invariants for level set functions, preprint, 2015.   pdf
  13. Grim, A., O'Connor, T., Olver, P.J., Shakiban, C., Slechta, R., and Thompson, R., Reassembly of three-dimensional jigsaw puzzles, Int. J. Image Graphics 16 (2016), 1650009.   pdf    Matlab routines
  14. Olver, P.J., The symmetry groupoid and weighted signature of a geometric object, J. Lie Theory 26 (2015), 235-267.   pdf
  15. Kogan, I.A., and Olver, P.J., Invariants of objects and their images under surjective maps, Lobachevskii J. Math. 36 (2015), 260-285.   Corrected version: pdf   Corrections and additions to published version: pdf
  16. Olver, P.J., Modern developments in the theory and applications of moving frames, London Math. Soc. Impact150 Stories 1 (2015), 14-50.   pdf
  17. Hoff, D., and Olver, P.J., Automatic solution of jigsaw puzzles, J. Math. Imaging Vision 49 (2014), 234-250.   Corrected version: pdf   Corrections to published version: pdf     Matlab routines
  18. Hoff, D., and Olver, P.J., Extensions of invariant signatures for object recognition, J. Math. Imaging Vision 45 (2013), 176-185.   Corrected version: pdf   Corrections to published version: pdf     Matlab routines
  19. Brinkman, D., and Olver, P.J., Invariant histograms, Amer. Math. Monthly 119 (2012), 4-24.   pdf
  20. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  21. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  22. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  23. Rathi, Y., Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant surface evolutions for 3D image segmentation, in: Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, E.R. Dougherty, J.T. Astola, K.O. Egiazarian, N.M. Nasrabadi, and S.A. Rizvi, eds., vol. 6064, SPIE Press, Bellingham, Wash., 2006, pp. 606401.   pdf
  24. Georgiou, T., Olver, P.J., and Tannenbaum, A., Maximal entropy for reconstruction of back projection images, in: Mathematical Methods in Computer Vision, P.J. Olver and A. Tannenbaum, eds., IMA Volumes in Mathematics and its Applications, vol. 133, Springer-Verlag, New York, 2003, pp. 57-64.   pdf
  25. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  26. Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S., Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision 26 (1998), 107-135.   Corrected version: pdf   Corrections to published version: pdf
  27. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant gradient flows, in: ICAOS '96: Images, Wavelets and PDE's, M.-O. Berger, et. al., eds., Lecture Notes in Control and Information Sciences, vol. 219, Springer-Verlag, New York, 1996, pp. 194-200.   pdf
  28. Calabi, E., Olver, P.J., and Tannenbaum, A., Invariant numerical approximations to differential invariant signatures, preprint, University of Minnesota, 1995.   pdf
  29. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edge maps, anisotropic diffusion, and active contours, Acta Appl. Math. 59 (1999), 45-77.   pdf
  30. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edges, active contours, and segments, in: Proceedings 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings, IEEE Computer Soc. Press, Los Alamitos, CA, 1996, pp. 520-525.   pdf
  31. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A., A gradient surface evolution approach to 3D segmentation, in: Proceedings of the IS&T's 49th Annual Conference; Society for Imaging Science and Technology, Springfield, Virginia, 1996, pp. 305-307   pdf
  32. Kumar, A., Yezzi, A., Kichenassamy, S., Olver, P.J., Tannenbaum, A., Active contours for visual tracking: a geometric gradient based approach, in: Proceedings of the 34th Conference on Decision and Control, IEEE Computer Soc. Press, Piscataway, N.J., 1995, pp. 4041-4046.   pdf
  33. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P.J., and Tannenbaum, A., A geometric snake model for segmentation of medical imagery, IEEE Trans. Medical Imaging 16 (1997), 199-209.   pdf
  34. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996), 154-196.   Corrected version: pdf   Correction to published version: pdf
  35. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Conformal curvature flows: from phase transitions to active vision, Arch. Rat. Mech. Anal. 134 (1996), 275-301.   pdf
  36. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Gradient flows and geometric active contour models, in: Fifth International Conference on Computer Vision, IEEE Computer Soc. Press, Cambridge, Mass., 1995, pp. 810-815.   pdf
  37. Olver, P.J., Sapiro, G., and Tannenbaum, A., Invariant geometric evolutions of surfaces and volumetric smoothing, SIAM J. Appl. Math. 57 (1997), 176-194.   pdf
  38. Olver, P.J., Sapiro, G., and Tannenbaum, A., Differential invariant signatures and flows in computer vision: a symmetry group approach, in: Geometry-Driven Diffusion in Computer Vision, B.M. Ter Haar Romeny, ed., Kluwer Acad. Publ., Dordrecht, Netherlands, 1994, pp. 255-306.   pdf
  39. Olver, P.J., Sapiro, G., and Tannenbaum, A., Classification and uniqueness of invariant geometric flows, Comptes Rendus Acad. Sci. (Paris), Série I, 319 (1994), 339-344.   pdf

Symmetry, Lie groups, Lie algebras

  1. Olver, P.J., On the structure and generators of differential invariant algebras, in: Computer Algebra in Scientific Computing, F. Boulier, M. England, I. Kotsireas, T.M. Sadykov, E.V. Vorozhtsov, eds., Lecture Notes in Computer Science, vol. 14139, Springer-Verlag, New York, 2023, pp. 292-311.   pdf
  2. Olver, P.J., Higher order symmetries of underdetermined systems of partial differential equations and Noether's second theorem, Stud. Appl. Math. 147 (2021) 904-913.   pdf
  3. Olver, P.J., Divergence invariant variational problems, in: The Philosophy and Physics of Noether's Theorems, J. Read and N.J. Teh, eds., Cambridge University Press, Cambridge, UK, 2022, pp. 134-143.   pdf
  4. Barral, D., Bencheikh, K., Olver, P.J., Belabas, N., Levenson, J.A.; Symmetry-based analytical solutions to the χ(2) nonlinear directional coupler, Phys. Rev. E 99 (2019) 042211.   pdf
  5. Olver, P.J., Emmy Noether's enduring legacy in symmetry, Symmetry: Culture and Science 29 (2018) 475-485.  pdf
  6. Ruiz, A., Muriel, C., and Olver, P.J., On the commutator of C∞ symmetries and the reduction of Euler-Lagrange equations, J. Phys. A 51 (2018) 145202.  pdf
  7. Olver, P.J., The symmetry groupoid and weighted signature of a geometric object, J. Lie Theory 26 (2015), 235-267.   pdf
  8. Olver, P.J., Invariant variational problems and invariant flows via moving frames, in: Variations, Geometry and Physics, O. Krupková, and D. Saunders, eds., Nova Science Publ., New York, 2009, pp. 209-235.   pdf
  9. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  10. Cheh, J., Olver, P.J., and Pohjanpelto, J., Algorithms for differential invariants of symmetry groups of differential equations, Found. Comput. Math. 8 (2008), 501-532.   pdf
  11. Muriel, C., Romero, J.L., and Olver, P.J., Variational C∞ symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006), 164-184.   pdf
  12. Cheh, J., Olver, P.J., and Pohjanpelto, J., Maurer-Cartan equations for Lie symmetry pseudo-groups of differential equations, J. Math. Phys., 46 (2005), 023504.   pdf
  13. Olver, P.J., Nonlocal symmetries and ghosts, in: New Trends in Integrability and Partial Solvability, A.B. Shabat et. al., eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2004, pp. 199-215.   pdf
  14. Olver, P.J., Sanders, J., and Wang, J.P., Ghost symmetries, J. Nonlinear Math. Phys. 9, Suppl. 1 (2002), 164-172.   pdf
  15. Kogan, I.A., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001), 131-144.   Corrected version: pdf   Corrections to published version: pdf
  16. Kogan, I.A., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003), 137-193.   Corrected version: pdf   Corrections to published version: pdf
  17. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.   pdf
  18. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.   pdf
  19. Foursov, M.V., Olver, P.J., and Reyes, E.G., On formal integrability of evolution equations and local geometry of surfaces, Diff. Geom. Appl., 15 (2001), 183-199.   pdf
  20. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   Updated version: pdf   Updates to published version: pdf
  21. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.   pdf
  22. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000), 566-586.   pdf
  23. Kamran, N., Milson, R., and Olver, P.J., Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems, Adv. in Math. 156 (2000), 286-319.   pdf
  24. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998), L5-L8.   pdf
  25. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998), 245-268.   pdf
  26. Heredero, R.H., Olver, P.J., Classification of invariant wave equations, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 2, H.-D. Doebner, W. Scherer, C. Schulte, eds., World Scientific, Singapore, 1997, pp. 1010-1016.   pdf
  27. Heredero, R.H., and Olver, P.J., Classification of invariant wave equations, J. Math. Phys. 37 (1996), 6414-6438.   pdf
  28. Olver, P.J., and Vorob'ev, E.M., Nonclassical and conditional symmetries, in: CRC Handbook of Lie Group Analysis of Differential Equations, vol. 3, N.H. Ibragimov, ed., CRC Press, Boca Raton, Fl., 1996, pp. 291-328.   pdf
  29. Olver, P.J., Non-associative local Lie groups, J. Lie Theory 6 (1996), 23-51.   Corrected version: pdf   Correction to published version: pdf
  30. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.   pdf
  31. Clarkson, P.A., and Olver, P.J., Symmetry and the Chazy equation, J. Diff. Eq. 124 (1996), 225-246.   pdf
  32. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.   pdf
  33. Anderson, I.M., Kamran, N., and Olver, P.J., Internal symmetries of differential equations, in: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N.H. Ibragimov, M. Torrisi, and A. Valenti, eds., Kluwer, Dordrecht, Netherlands, 1993, pp. 7-21.   pdf
  34. Olver, P.J., Direct reduction and differential constraints, Proc. Roy. Soc. London A 444 (1994), 509-523.   pdf
  35. Olver, P.J., Symmetry and explicit solutions of partial differential equations, Appl. Numerical Math. 10 (1992), 307-324.   pdf
  36. Olver, P.J., Internal symmetries of differential equations, in: Differential Equations and Computer Algebra, M. Singer, ed., Academic Press, New York, 1991, pp. 1-28.   
  37. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.   pdf
  38. Anderson, I.M., Kamran, N., and Olver, P.J., Internal, external and generalized symmetries, Adv. in Math. 100 (1993), 53-100.   pdf
  39. González-López, A., Kamran, N., and Olver, P.J., Lie algebras of vector fields in the real plane, Proc. London Math. Soc. 64 (1992), 339-368.   pdf
  40. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.   Scanned:  pdf
  41. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.    pdf
  42. Olver, P.J., Generalized symmetries, in: XV International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed., World Scientific, Singapore, 1987, pp. 216-228.   
  43. Olver, P.J., and Rosenau, P., Group-invariant solutions of differential equations, SIAM J. Appl. Math. 47 (1987), 263-278.   pdf
  44. Olver, P.J., and Rosenau, P., The construction of special solutions to partial differential equations, Phys. Lett. 114A (1986), 107-112.   pdf
  45. Olver, P.J., Noether's theorems and systems of Cauchy-Kovalevskaya type, in: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, B. Nicholaenko, D.D. Holm and J.M. Hyman, eds., Lectures in Applied Math., vol. 23, part 2, Amer. Math. Soc., Providence, R.I., 1986, pp. 81-104.   Scanned:  pdf
  46. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
  47. Olver, P.J., How to find the symmetry group of a differential equation, appendix in: Group Theoretic Methods in Bifurcation Theory, D.H. Sattinger, Lecture Notes in Mathematics, vol. 762, Springer-Verlag, New York, 1979.   pdf
  48. Olver, P.J., Symmetry groups and group invariant solutions of partial differential equations, J. Diff. Geom. 14 (1979), 497-542.   pdf
  49. Olver, P.J., Symmetry groups and conservation laws in the formal variational calculus, preprint, University of Oxford, 1978.   Scanned:  pdf
  50. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.   pdf
  51. Olver, P.J., Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215. Reprinted in: Solitons and Particles, C. Rebbi and G. Soliani, eds., World Scientific, Singapore, 1984, pp. 235-238.   pdf
  52. Olver, P.J., On the symmetry group of a linear partial differential equation, preprint, University of Chicago, 1977.   Scanned:  pdf
  53. Olver, P.J., Symmetry groups of partial differential equations, thesis, Harvard University, 1976.   Scanned:  pdf

Waves, Fluid Mechanics, Integrable Systems

  1. Farmakis, G., Kang, J., Olver, P.J., Qu, C., Yin, Z.; New revival phenomena for bidirectional dispersive hyperbolic equations, preprint, 2023.   pdf
  2. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences for integrable hierarchies, in: Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China, N. Euler and D.-J. Zhang, eds., CRC Press, 2022, pp. 102-134.   pdf
  3. Boulton, L., Olver, P.J., Pelloni, B., and Smith, D.A., New revival phenomena for linear integro-differential equations, Stud. Appl. Math. 147 (2021) 1209-1239.   pdf
  4. Olver, P.J., and Stern, A., Dispersive fractalization in Fermi-Pasta-Ulam-Tsingou lattices, European J. Appl. Math. 32 (2021) 820-845.   pdf
  5. Olver, P.J., Sheils, N.E., and Smith, D.A., Revivals and fractalisation in the linear free space Schrödinger equation, Quart. Appl. Math. 78 (2020) 161-192.   pdf      movies
  6. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences between multi-component integrable hierarchies, Theor. Math. Phys. 204 (2020) 843-874.   pdf
  7. Olver, P.J., and Tsatis, E., Points of constancy of the periodic linearized Korteweg-deVries equation, Proc. Roy. Soc. London A 474 (2018) 20180160.   pdf
  8. Olver, P.J., and Sheils, N.E., Dispersive Lamb systems, J. Geom. Mech. 11 (2019) 239-254.   pdf      movies
  9. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences between integrable hierarchies, SIGMA: Symmetry Integrability Geom. Methods Appl. 13 (2017), 035.   pdf
  10. Kang, J., Liu, X., Olver, P.J., and Qu, C., Bäcklund transformations for tri-Hamiltonian dual structures of multi-component integrable systems, J. Integ. Sys. 2 (2017), xyw016.   pdf
  11. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy, J. Nonlinear Science 26 (2016), 141-170.   pdf
  12. Liu, Y., Olver, P.J., Qu, C., and Zhang, S.; On the blow-up of solutions to the integrable modified Camassa-Holm equation, Analysis Appl. 12 (2014), 355-368.   pdf
  13. Liu, X., Liu, Y., Olver, P.J., and Qu, C., Orbital stability of peakons for a generalization of the modified Camassa-Holm equation, Nonlinearity 27 (2014), 2297-2319.   pdf
  14. Chen, G., and Olver, P.J., Numerical simulation of nonlinear dispersive quantization, Discrete Cont. Dyn. Syst. A 34 (2013), 991-1008.   pdf
  15. Chen, G., and Olver, P.J., Dispersion of discontinuous periodic waves, Proc. Roy. Soc. London A 469 (2012), 20120407.   pdf
  16. Gui, G., Liu, Y., Olver, P.J., and Qu, C., Wave-breaking and peakons for a modified Camassa-Holm equation, Commun. Math. Phys. 319 (2013), 731-759.   pdf
  17. Olver, P.J., Dispersive quantization, Amer. Math. Monthly 117 (2010), 599-610.   Corrected version: pdf   Corrections to published version: pdf
  18. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  19. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA: Symmetry Integrability Geom. Methods Appl. 2 (2006), 054.   pdf
  20. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.   pdf
  21. Foursov, M.V., Olver, P.J., and Reyes, E.G., On formal integrability of evolution equations and local geometry of surfaces, Diff. Geom. Appl., 15 (2001), 183-199.   pdf
  22. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.   pdf
  23. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000), 566-586.   pdf
  24. Li, Y.A., and Olver, P.J., Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Diff. Eq. 162 (2000), 27-63.   pdf
  25. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998), L5-L8.   pdf
  26. Li, Y.A., Olver, P.J., and Rosenau, P., Non-analytic solutions of nonlinear wave equations, in: Nonlinear Theory of Generalized Functions, M. Grosser, G. Hormann, M. Kunzinger, and M. Oberguggenberger, eds., Research Notes in Mathematics, vol. 401, Chapman and Hall/CRC, New York, 1999, pp. 129-145.   pdf
  27. Gunney, B.T.N., Li, Y.A., and Olver, P.J., Solitary waves in the critical surface tension model, J. Engin. Sci. 36 (1999), 99-112.   pdf
  28. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998), 245-268.   pdf
  29. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II. Complex analytic behavior and convergence to non-analytic solutions, Discrete Cont. Dyn. Syst. 4 (1998), 159-191.   pdf
  30. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons, Discrete Cont. Dyn. Syst. 3 (1997), 419-432.   pdf
  31. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.   pdf
  32. Olver, P.J., and Rosenau, P., Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E 53 (1996), 1900-1906.   pdf
  33. Olver, P.J., Higher order models for water waves, in: Geometrical Methods in Fluid Dynamics, R. Salmon, B. Ewing-Deremer, eds., Woods Hole Oceanographic Institution, Technical Report WHOI-94-12, Woods Hole, MA, 1994, pp. 327-331.   Scanned:  pdf
  34. Kichenassamy, S., and Olver, P.J., Existence and non-existence of solitary wave solutions to higher order model evolution equations, SIAM J. Math. Anal. 23 (1992), 1141-1166.   pdf
  35. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.   pdf
  36. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.   pdf
  37. Clarkson, P., McLeod, J.B., Olver, P.J., and Ramani, A., Integrability of Klein-Gordon equations, SIAM J. Math. Anal. 17 (1986), 798-802.   pdf
  38. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.   Scanned:  pdf
  39. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.   Scanned:  pdf
  40. Olver, P.J., Conservation laws of free boundary problems and the classification of conservation laws for water waves, Trans. Amer. Math. Soc. 277 (1983), 353-380.   pdf
  41. McLeod, J.B., and Olver, P.J., The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of Painlevé type, SIAM J. Math. Anal. 14 (1983), 488-506.   pdf
  42. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.   pdf
  43. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.   pdf
  44. Olver, P.J., On the construction of deformations of integrable systems, preprint, University of Minnesota, 1981.   Scanned:  pdf
  45. Olver, P.J., Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 (1979), 143-160.   pdf
  46. Olver, P.J., Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215. Reprinted in: Solitons and Particles, C. Rebbi and G. Soliani, eds., World Scientific, Singapore, 1984, pp. 235-238.   pdf

Hamiltonian Systems

  1. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences between multi-component integrable hierarchies, Theor. Math. Phys. 204 (2020) 843-874.   pdf
  2. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondences between integrable hierarchies, SIGMA: Symmetry Integrability Geom. Methods Appl. 13 (2017), 035.   pdf
  3. Kang, J., Liu, X., Olver, P.J., and Qu, C., Bäcklund transformations for tri-Hamiltonian dual structures of multi-component integrable systems, J. Integ. Sys. 2 (2017), xyw016.   pdf
  4. Kang, J., Liu, X., Olver, P.J., and Qu, C., Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy, J. Nonlinear Science 26 (2016), 141-170.   pdf
  5. Fernandez, O.E., Bloch, A.M., and Olver, P.J., Variational integrators for Hamiltonizable nonholonomic systems, J. Geom. Mech. 4 (2012), 137-163.   pdf
  6. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA: Symmetry Integrability Geom. Methods Appl. 2 (2006), 054.   pdf
  7. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999), 807-839.   pdf
  8. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.   pdf
  9. Olver, P.J., and Rosenau, P., Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E 53 (1996), 1900-1906.   pdf
  10. Olver, P.J., Canonical forms for biHamiltonian systems, in: The Verdier Memorial Conference on Integrable Systems, O. Babelon, P. Cartier and Y. Kosmann-Schwarzbach eds., Progress in Math., Birkhäuser, Boston, 1993, pp. 239-249.    pdf
  11. Olver, P.J., Canonical forms for compatible biHamiltonian systems, in: Solitons and Chaos, I. Antoniou and F. Lambert, eds., Springer-Verlag, New York, 1991, pp. 171-179.   Scanned:  pdf
  12. Olver, P.J., Canonical forms and integrability of biHamiltonian systems, Phys. Lett. 148A (1990), 177-187.   pdf
  13. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.    pdf
  14. Arik, M., Neyzi, F., Nutku, Y., Olver, P.J., and Verosky, J.M., Multi-Hamiltonian structure of the Born-Infeld equation, J. Math. Phys. 30 (1989), 1338-1344.    pdf
  15. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.    pdf
  16. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.   Scanned:  pdf
  17. Olver, P.J., and Nutku, Y., Hamiltonian structures for systems of hyperbolic conservation laws, J. Math. Phys. 29 (1988), 1610-1619.   pdf
  18. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.   pdf
  19. Olver, P.J., BiHamiltonian systems, in: Ordinary and Partial Differential Equations, B.D. Sleeman and R.J. Jarvis, eds., Pitman Research Notes in Mathematics Series, No. 157, Longman Scientific and Technical, New York, 1987, pp. 176-193.   Scanned:  pdf
  20. Olver, P.J., Darboux' theorem for Hamiltonian differential operators, J. Diff. Eq. 71 (1988), 10-33.   pdf
  21. Olver, P.J., Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators, J. Math. Phys. 27 (1986), 2495-2501.   pdf
  22. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.   Scanned:  pdf
  23. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.   Scanned:  pdf
  24. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.   pdf
  25. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.   pdf
  26. Olver, P.J., On the Hamiltonian structure of evolution equations, Math. Proc. Camb. Phil. Soc. 88 (1980), 71-88.   pdf

Calculus of Variations

  • Olver, P.J., Boundary conditions and null Lagrangians in the calculus of variations and elasticity, J. Elasticity 155 (2024) 75-108.   pdf
  • Olver, P.J., Divergence invariant variational problems, in: The Philosophy and Physics of Noether's Theorems, J. Read and N.J. Teh, eds., Cambridge University Press, Cambridge, UK, 2022, pp. 134-143.   pdf
  • Olver, P.J., Emmy Noether's enduring legacy in symmetry, Symmetry: Culture and Science 29 (2018) 475-485.  pdf
  • Olver, P.J., Invariant variational problems and invariant flows via moving frames, in: Variations, Geometry and Physics, O. Krupková, and D. Saunders, eds., Nova Science Publ., New York, 2009, pp. 209-235.   pdf
  • Muriel, C., Romero, J.L., and Olver, P.J., Variational C∞ symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006), 164-184.   pdf
  • Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001), 131-144.   Corrected version: pdf   Corrections to published version: pdf
  • Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003), 137-193.   Corrected version: pdf   Corrections to published version: pdf
  • Olver, P.J., Equivalence and the Cartan form, Acta Applicandae Math. 31 (1993), 99-136.   pdf
  • Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians III. New invariant differential equations, Nonlinearity 5 (1992), 601-621.   pdf
  • Hsu, L., Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians II. The Cartan form for particle Lagrangians, J. Math. Phys. 30 (1989), 902-906.   pdf
  • Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians I. Formulation and reduction, J. Math. Pures et Appliquees 70 (1991), 369-391.   pdf
  • Kamran, N., and Olver, P.J., Le probleme d'équivalence à une divergence près dans le calcul des variations des intégrales multiples, Comptes Rendus Acad. Sci. (Paris), Série I, 308 (1989), 249-252.   Scanned:  pdf
  • Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
  • Kamran, N., and Olver, P.J., Equivalence problems for first order Lagrangians on the line, J. Diff. Eq. 80 (1989), 32-78.   pdf
  • Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.   pdf
  • Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.   pdf
  • Olver, P.J., and Sivaloganathan, J., The classification of null Lagrangians, Nonlinearity 1 (1988), 389-398.   pdf
  • Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.   pdf
  • Olver, P.J., Noether's theorems and systems of Cauchy-Kovalevskaya type, in: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, B. Nicholaenko, D.D. Holm and J.M. Hyman, eds., Lectures in Applied Math., vol. 23, part 2, Amer. Math. Soc., Providence, R.I., 1986, pp. 81-104.   Scanned:  pdf
  • Olver, P.J., Conservation laws and null divergences II. Nonnegative divergences, Math. Proc. Camb. Phil. Soc. 97 (1985), 511-514.   pdf
  • Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
  • Olver, P.J., Conservation laws and null divergences, Math. Proc. Camb. Phil. Soc. 94 (1983), 529-540.   pdf
  • Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.   S pdf
  • Ball, J.M., Currie, J.C., and Olver, P.J., Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Func. Anal. 41 (1981), 135-174.   pdf
  • Olver, P.J., Symmetry groups and conservation laws in the formal variational calculus, preprint, University of Oxford, 1978.   Scanned:  pdf
  • Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.   pdf

    Elasticity and Continuum Mechanics

    1. Olver, P.J., Boundary conditions and null Lagrangians in the calculus of variations and elasticity, J. Elasticity 155 (2024) 75-108.   pdf
    2. Bozhkov, Y., and Olver, P.J., Pohozhaev and Morawetz identities in elastostatics and elastodynamics, SIGMA: Symmetry Integrability Geom. Methods Appl. 7 (2011), 055.   pdf
    3. Hatfield, G.A., and Olver, P.J., Canonical forms and conservation laws in linear elastostatics, Arch. Mech. 50 (1998), 389-404.   pdf
    4. Olver, P.J., Canonical anisotropic elastic moduli, in: Modern Theory of Anisotropic Elasticity and Applications, J.J. Wu, T.C.T. Ting and D.M. Barnett, eds., SIAM, Philadelphia, 1991, pp. 325-339.   Scanned:  pdf
    5. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.    pdf
    6. Olver, P.J., and Sivaloganathan, J., The classification of null Lagrangians, Nonlinearity 1 (1988), 389-398.   pdf
    7. Olver, P.J., Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rat. Mech. Anal. 102 (1988), 167-181.   pdf
    8. Olver, P.J., Canonical elastic moduli, J. Elasticity 19 (1988), 189-212.   pdf
    9. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.   pdf
    10. Olver, P.J., Conservation laws in continuum mechanics, in: Non-classical Continuum Mechanics, R.J. Knops and A.A. Lacey, eds., London Math. Soc. Lecture Note Series #122, Cambridge Univ. Press, Cambridge, 1987, pp. 96-107.   Scanned:  pdf
    11. Olver, P.J., Conservation laws and null divergences II. Nonnegative divergences, Math. Proc. Camb. Phil. Soc. 97 (1985), 511-514.   pdf
    12. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
    13. Olver, P.J., Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics, Arch Rat. Mech. Anal. 85 (1984), 131-160.   pdf   Errata, Arch Rat. Mech. Anal., 102 (1988), 385-387.   pdf
    14. Olver, P.J., Conservation laws in elasticity. I. General results, Arch Rat. Mech. Anal. 85 (1984), 111-129.   pdf
    15. Olver, P.J., Group-theoretic classification of conservation laws in elasticity, in: Systems of Nonlinear Partial Differential Equations, J.M. Ball, ed., D. Reidel, Boston, 1983, pp. 323-331.   pdf
    16. Olver, P.J., Conservation laws and null divergences, Math. Proc. Camb. Phil. Soc. 94 (1983), 529-540.   pdf
    17. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.   S pdf
    18. Ball, J.M., Currie, J.C., and Olver, P.J., Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Func. Anal. 41 (1981), 135-174.   pdf

    Quantum Mechanics and Physics

    1. Olver, P.J., Motion and continuity, Math. Intelligencer 44 (2022) 241-249.   pdf
    2. Barral, D., Bencheikh, K., Olver, P.J., Belabas, N., Levenson, J.A.; Symmetry-based analytical solutions to the χ(2) nonlinear directional coupler, Phys. Rev. E 99 (2019) 042211.   pdf
    3. Grinberg, D., and Olver, P.J., The n body matrix and its determinant, SIAM J. Appl. Algebra Geometry 3 (2019) 67-86.   pdf
    4. Chen, G., and Olver, P.J., Numerical simulation of nonlinear dispersive quantization, Discrete Cont. Dyn. Syst. A 34 (2013), 991-1008.   pdf
    5. Chen, G., and Olver, P.J., Dispersion of discontinuous periodic waves, Proc. Roy. Soc. London A 469 (2012), 20120407.   pdf
    6. Olver, P.J., Dispersive quantization, Amer. Math. Monthly 117 (2010), 599-610.   Corrected version: pdf   Corrections to published version: pdf
    7. Kamran, N., Milson, R., and Olver, P.J., Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems, Adv. in Math. 156 (2000), 286-319.   pdf
    8. Olver, P.J., A quasi-exactly solvable travel guide, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 1, H.-D. Doebner, W. Scherer, and P. Nattermann, eds., World Scientific, Singapore, 1997, pp. 285-295.   pdf
    9. Finkel, F., González-López, A., Kamran, N., Olver, P.J., and Rodriguez, M.A., Lie algebras of differential operators and partial integrability, in: Proceedings of IV Workshop on Differential Geometry and its Applications; Santiago de Compostela, Spain, 1995.   pdf
    10. González-López, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in the real domain, preprint, University of Minnesota, 1995.   pdf
    11. González-López, A., Kamran, N., and Olver, P.J., Real Lie algebras of differential operators, and quasi-exactly solvable potentials, Phil. Trans. Roy. Soc. London A 354 (1996), 1165-1193.   pdf
    12. González-López, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in higher dimensions, appendix in: Quasi-Exact Solvability; A.G. Ushveridze, Adam Hilger, Bristol, 1994.   
    13. González-López, A., Kamran, N., and Olver, P.J., Quasi-exact solvability, Contemp. Math. 160 (1994), 113-140.   pdf
    14. González-López, A., Hurturbise, J., Kamran, N., and Olver, P.J., Quantification de la cohomologie des algèbres de Lie de champs de vecteurs et fibrés en droites sur des surfaces complexes compactes, Comptes Rendus Acad. Sci. (Paris), Série I, 316 (1993), 1307-1312.   Scanned:  pdf
    15. González-López, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, in: Group Theoretic Methods in Physics, M.A. del Olmo, M. Santander, and J. Mateos Guilarte, eds., Proc. XIX International Colloquium, Anales de Física Monografias, Editorial Ciemat, Madrid, 1992, Vol. I, pp. 233-236.   pdf
    16. González-López, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, Commun. Math. Phys. 159 (1994), 503-537.   pdf
    17. González-López, A., Kamran, N., and Olver, P.J., Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators, Commun. Math. Phys. 153 (1993), 117-146.   pdf
    18. González-López, A., Kamran, N., and Olver, P.J., Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables, J. Phys. A 24 (1991), 3995-4008.   pdf
    19. González-López, A., Kamran, N., and Olver, P.J., Lie algebras of first order differential operators in two complex variables, in: Differential Geometry, Global Analysis, and Topology, A. Nicas and W.F. Shadwick, eds., Canadian Math. Soc. Conference Proceedings, vol. 12, Amer. Math. Soc., Providence, R.I., 1991, pp. 51-84.   
    20. González-López, A., Kamran, N., and Olver, P.J., Lie algebras of vector fields in the real plane, Proc. London Math. Soc. 64 (1992), 339-368.   pdf
    21. González-López, A., Kamran, N., and Olver, P.J., Lie algebras of differential operators in two complex variables, American J. Math. 114 (1992), 1163-1185.   pdf
    22. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.   pdf
    23. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.   pdf
    24. Kamran, N., and Olver, P.J., Lie algebras of differential operators and Lie-algebraic potentials, J. Math. Anal. Appl. 145 (1990), 342-356.   pdf
    25. Olver, P.J., Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators, J. Math. Phys. 27 (1986), 2495-2501.   pdf

    Invariant Theory, Algebra, Number Theory

    1. Olver, P.J., Invariants of finite and discrete group actions via moving frames, Bull. Iranian Math. Soc. 49 (2023) 11.   pdf
    2. Grinberg, D., and Olver, P.J., The n body matrix and its determinant, SIAM J. Appl. Algebra Geometry 3 (2019) 67-86.   pdf
    3. Olver, P.J., and Tsatis, E., Points of constancy of the periodic linearized Korteweg-deVries equation, Proc. Roy. Soc. London A 474 (2018) 20180160.   pdf
    4. Gün Polat, G., and Olver, P.J., Joint differential invariants of binary and ternary forms, Portugaliae Math. 76 (2019) 169-204.   Corrected version: pdf   Corrections and additions to published version: pdf
    5. Olver, P.J., Modern developments in the theory and applications of moving frames, London Math. Soc. Impact150 Stories 1 (2015), 14-50.   pdf
    6. Olver, P.J., Petitot, M., Solé, P., Generalized transvectants and Siegel modular forms, Adv. Appl. Math. 38 (2007), 404-418.   pdf
    7. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
    8. Olver, P.J., Lie algebras and Lie groups, in: Encyclopedia of Nonlinear Science, A. Scott, ed., Routledge, New York, New York, 2005, pp. 526-528.   pdf
    9. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
    10. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.   pdf
    11. Olver, P.J., and Sanders, J., Transvectants, modular forms, and the Heisenberg algebra, Adv. Appl. Math. 25 (2000), 252-283.   pdf
    12. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000), 485-514.   pdf
    13. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997), 701-732.   pdf
    14. Maliakis, M., and Olver, P.J., Explicit generalized Pieri maps, J. Algebra 148 (1992), 68-85.   pdf
    15. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
    16. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.   pdf
    17. Olver, P.J., and Shakiban, C., Graph theory and classical invariant theory, Adv. in Math. 75 (1989), 212-245.   pdf
    18. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.   pdf
    19. Olver, P.J., Invariant theory of biforms, preprint, University of Minnesota, 1986.   Scanned:  pdf
    20. Olver, P.J., Invariant theory and differential equations, in: Invariant Theory, S.S. Koh, ed., Lecture Notes in Mathematics, vol. 1278, Springer-Verlag, New York, 1987, pp. 62-80.   Scanned:  pdf
    21. Olver, P.J., Differential hyperforms I, preprint, University of Minnesota, 1982.   Scanned:  pdf
    22. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.    pdf

    Numerical Analysis

    1. Olver, P.J., and Stern, A., Dispersive fractalization in Fermi-Pasta-Ulam-Tsingou lattices, European J. Appl. Math. 32 (2021) 820-845.   pdf
    2. Chen, G., and Olver, P.J., Numerical simulation of nonlinear dispersive quantization, Discrete Cont. Dyn. Syst. A 34 (2013), 991-1008.   pdf
    3. Chen, G., and Olver, P.J., Dispersion of discontinuous periodic waves, Proc. Roy. Soc. London A 469 (2012), 20120407.   pdf
    4. Fernandez, O.E., Bloch, A.M., and Olver, P.J., Variational integrators for Hamiltonizable nonholonomic systems, J. Geom. Mech. 4 (2012), 137-163.   pdf
    5. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
    6. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
    7. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004), 213-226.   pdf
    8. Olver, P.J., On multivariate interpolation, Stud. Appl. Math. 116 (2006), 201-240.   Corrected version: pdf   Corrections to published version: pdf
    9. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005), 341-374.   pdf
    10. Lewis, D., and Olver, P.J., Geometric integration algorithms on homogeneous manifolds, Found. Comput. Math. 2 (2002), 363-392.   pdf
    11. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
    12. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   Updated version: pdf   Updates to published version: pdf
    13. Gunney, B.T.N., Li, Y.A., and Olver, P.J., Solitary waves in the critical surface tension model, J. Engin. Sci. 36 (1999), 99-112.   pdf
    14. Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S., Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision 26 (1998), 107-135.   Corrected version: pdf   Corrections to published version: pdf
    15. Calabi, E., Olver, P.J., and Tannenbaum, A., Invariant numerical approximations to differential invariant signatures, preprint, University of Minnesota, 1995.   pdf
    16. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996), 154-196.   Corrected version: pdf   Correction to published version: pdf
    17. Olver, P.J., Some applications of spline functions to problems in computer graphics, senior honors thesis, Brown University, 1973.   Scanned:  pdf

    Analysis

    1. Olver, P.J., Boundary conditions and null Lagrangians in the calculus of variations and elasticity, J. Elasticity 155 (2024) 75-108.   pdf
    2. Olver, P.J., Motion and continuity, Math. Intelligencer 44 (2022) 241-249.   pdf
    3. Malkoun, J., and Olver, P.J., Continuous maps from spheres converging to boundaries of convex hulls, Forum Math. Sigma 9 (2021) e13.   pdf     Python routines
    4. Olver, P.J., and Raphael, R., The absolute value of functions, Real Analysis Exchange, 25 (1999/2000), 257-290.   pdf
    5. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.   pdf
    6. Olver, P.J., A nonlinear differential operator series which commutes with any function, SIAM J. Math. Anal. 23 (1992), 209-221.   pdf
    7. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.    pdf