KP-II APPROXIMATION FOR A SCALAR FERMI--PASTA--ULAM

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.

Automated summary

This paper investigates a scalar Fermi-Pasta-Ulam (FPU) system on a square two-dimensional lattice. The Kadomtsev-Petviashvili (KP-II) equation is derived using multiple scale expansions, and it accurately describes the dynamics of small-amplitude, slowly varying, unidirectional long waves on the FPU system. The main novelty of this work lies in the utilization of Fourier transform in the analysis of the FPU system in strain variables.