We consider the equation \[\tag{1}
\Delta u+u_{yy}+f(x,u)=0,\quad (x,y)\in\mathbb{R}^{N}\times \mathbb{R}
\] where $f$ is sufficiently regular, radially symmetric in $x$, and $f(\cdot,0)\equiv 0$. We give sufficient conditions for the existence of solutions of (1) which are quasiperiodic in $y$ and decaying as $|x|\to\infty$ uniformly in $y$. Such solutions are found using a center manifold reduction, and results from the KAM theory. The required nondegeneracy condition is stated in terms of $f_u(x,0)$ and $f_{uu}(x,0)$, and is independent of higher-order terms in the Taylor expansion of $f(x,\cdot)$. In particular, our results apply to some quadratic nonlinearities.