  We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D 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 scalar 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 Fourier transform in
the analysis of the FPU system in strain variables.
