Method for searching higher symmetries for quad graph equations

TL;DR

This paper introduces a method to identify higher symmetries in quad graph equations, enhancing the understanding of their integrability by using characteristic vector fields.

Contribution

It proposes a novel approach for searching higher symmetries, including non-autonomous ones, for discrete equations on the square lattice.

Findings

Developed a generalized symmetry integrability test.

Discussed integrability conditions for discrete equations.

Suggested a new method based on characteristic vector fields.

Abstract

Generalized symmetry integrability test for discrete equations on the square lattice is studied. Integrability conditions are discussed. A method for searching higher symmetries (including non-autonomous ones) for quad graph equations is suggested based on characteristic vector fields.