High order multiscale analysis of discrete integrable equations

2013/11/08 by Rafael Hernández Heredero, Heredero, R. Hernandez, D. Levi +3
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1311.1905

Abstract

In this article we present the results obtained applying the multiple scale expansion up to the order ε⁶ 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 are new, depending at most on 2 parameters and containing integrable sub cases. Moreover at least one sub case provides an example of a new integrable system.

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