A Lax pair of a lattice equation whose entropy vanishes

TL;DR

This paper introduces a new Lax pair for a non-symmetric lattice equation derived from known integrable equations, highlighting its integrability and connection to entropy properties.

Contribution

The paper presents a novel Lax pair for a non-symmetric lattice equation obtained via a double twist and a limiting process, expanding the understanding of integrable lattice equations.

Findings

Derived a multi parametric quadgraph equation consistent around the cube.

Obtained a Lax pair for the non-symmetric equation by Hietarinta and Viallet.

Connected the equation's properties to entropy vanishing.

Abstract

In this paper, we present multi parametric quadgraph equations which are consistent around the cube. These equations are obtained by applying a `double twist' to known integrable equations. Furthermore, we perform a limit to one of these equations to derive the non-symmetric equation which is given by Hietarinta and Viallet. As a result, we obtain a novel Lax pair of this equation.