High order multiscale analysis of discrete integrable equations

Abstract

In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which seem to be new, depending at most on 2 parameters.

Keywords

• multiple scale
• integrable difference equations
• pacs: 02.30.ks, 02.30.ik, 02.30.mvmsc 4e13, 37k10, 39a14, 93b18
• [nlin.nlin-si]nonlinear sciences [physics]/exactly solvable and integrable systems [nlin.si]
• [math.math-mp]mathematics [math]/mathematical physics [math-ph]