High order multiscale analysis of discrete integrable equations

R. Hernandez Heredero; D. Levi; C. Scimiterna

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arXiv · 1311.1905

High order multiscale analysis of discrete integrable equations

R. Hernandez Heredero·D. Levi·C. Scimiterna

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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 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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R. Hernandez Heredero, D. Levi, C. Scimiterna. 2013-11-08. High order multiscale analysis of discrete integrable equations. https://arxiv.org/abs/1311.1905

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