Generalized symmetry integrability test for discrete equations on the square lattice

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.