Generalized symmetry integrability test for discrete equations on the square lattice

TL;DR

This paper introduces a new integrability test for discrete square lattice equations based on generalized symmetries, successfully proving the integrability of several previously unclassified equations.

Contribution

It develops a generalized symmetry-based integrability test and applies it to identify new integrable discrete equations beyond known classifications.

Findings

Proved 7 new integrable discrete equations

Identified equations different from the $Q_V$ and ABS list

Validated the effectiveness of the new integrability test

Abstract

We present an integrability test for discrete equations on the square lattice, which is based on the existence of a generalized symmetry. We apply this test to a number of equations obtained in different recent papers. As a result we prove the integrability of 7 equations which differ essentially from the $Q_V$ equation introduced by Viallet and thus from the Adler-Bobenko-Suris list of equations therein contained.