Movies of Dispersive Lamb Systems

Movies and Mathematica code connected with the paper

    Olver, P.J., and Sheils, N.E., Dispersive Lamb systems, preprint, 2017.  pdf

The following plots are all for a system that begins at rest with zero initial velocity: u(0,x)=u_t(,x)=0. Each plot is tagged by the associated dispersion relation.

The Mathematica document used to make these vidoes is available here. These videos are also available on YouTube.

The Bidirectional Lamb Model

The wave equation on the whole line:   ω=ck

The Periodic Lamb Model

The wave equation on a periodic domain:   ω=ck

Bidirectional Dispersive Lamb Models

Linearized Boussinesq on a periodic domain  ω=k2

Dispersive Klein-Gordon on a periodic domain:   ω=(c2k2+m2)1/2

Water wave dispersion on a periodic domain:   ω=(k tanh(k))1/2

Regularized Boussinesq on a periodic domain:   ω=c|k|/(1+εk2)1/2

Unidirectional Models

Transport:   ω=ck

Second Order:   ω=k2

Asymptotically Constant:   ω=k2/(1+k2/3)

Decaying Dispersion:   ω=1/k