Justification of the KP-II approximation in dynamics of two-dimensional FPU systems

Dynamics of the Fermi–Pasta–Ulam (FPU) system on a two-dimensional square lattice is considered in the limit of small-amplitude long-scale waves with slow transverse modulations. In the absence of transverse modulations, dynamics of such waves, even at an oblique angle with respect to the square lattice, is known to be described by the Korteweg–de Vries (KdV) equation. For the three basic directions (horizontal, vertical, and diagonal), we …