KP-II Approximation for a Scalar Fermi–Pasta–Ulam System on a 2D Square Lattice

We consider a scalar Fermi–Pasta–Ulam (FPU) system on a square two-dimensional lattice. The Kadomtsev–Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly varying transverse modulations. We show that the KP-II approximation makes correct predictions about the dynamics of the original FPU system. An existing approximation result is extended to an …