Integrability Test for Discrete Equations via Generalized Symmetries

TL;DR

This paper introduces integrability conditions for partial difference equations using formal symmetries, helping identify integrable equations within a class derived from multilinear dispersive difference equations.

Contribution

It develops a new method to test integrability of discrete equations based on generalized symmetries, applied to a specific class of multilinear dispersive difference equations.

Findings

Identified integrable equations within the studied class.

Established criteria for integrability based on formal symmetries.

Provided a systematic approach for analyzing discrete integrability.

Abstract

In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations obtained by the multiple scale analysis of the general multilinear dispersive difference equation defined on the square.