Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube

TL;DR

This paper introduces a method to derive Lax matrices for lattice equations satisfying the consistency-around-a-face-centered-cube (CAFCC) condition, providing new insights into integrability and expanding known classes of equations.

Contribution

The paper presents a novel method for deriving Lax matrices for CAFCC-satisfying equations, including both known and newly identified integrable lattice equations.

Findings

Derived new Lax matrices for CAFCC equations

Unified treatment of known and new lattice equations

Enhanced understanding of integrability conditions

Abstract

There is a recently discovered formulation of the multidimensional consistency integrability condition for lattice equations, called consistency-around-a-face-centered-cube(CAFCC), which is applicable to equations defined on a vertex and its four nearest neighbours on the square lattice. This paper introduces a method of deriving Lax matrices for the equations which satisfy CAFCC. This method gives novel Lax matrices for such equations, which include previously known equations of discrete Toda-, or Laplace-type, as well as newer equations which have only appeared in the context of CAFCC.