Backlund transformations for integrable lattice equations

TL;DR

This paper introduces new Backlund transformations for integrable lattice equations, revealing additional auto-BTs and inter-equation BTs that enhance understanding of their integrability and connections.

Contribution

The paper presents novel Backlund transformations for known integrable lattice equations, including additional auto-BTs and inter-equation BTs, expanding the tools for analyzing integrability.

Findings

Some equations admit additional auto-BTs with parameters

Pairs of distinct equations are connected via BTs

Enhances understanding of integrability structures

Abstract

We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Backlund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them.