On some class of partial difference equations admitting a zero-curvature representation

TL;DR

This paper identifies classes of higher order partial difference equations with zero-curvature representations, generalizing lattice potential KdV, and constructs integrable hierarchies and related differential-difference equations.

Contribution

It introduces new classes of integrable partial difference equations with zero-curvature representations and constructs associated hierarchies and Lax pairs.

Findings

Identified classes of higher order partial difference equations with zero-curvature representation

Constructed integrable hierarchies related to these equations

Derived non-evolutionary differential-difference equations with Lax pairs

Abstract

We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized symmetries for obtained class of partial difference equations. As a byproduct we also derive non-evolutionary differential-difference equations with their Lax pair representation which may be of potential interest.