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 arbitrary direction of wave propagation. The main novelty of this work is the use of a Fourier transform in the analysis of the FPU system in strain variables.