On Non-Point Invertible Transformations of Difference and Differential-Difference Equations

TL;DR

This paper fully characterizes non-point invertible transformations for difference equations on quad-graphs and their differential-difference analogues, enabling the construction of new integrable equations and auto-transformations.

Contribution

It provides a complete description of non-point invertible transformations for specific classes of difference and differential-difference equations, expanding the tools for integrability analysis.

Findings

Complete description of non-point invertible transformations

Construction of new integrable equations

Development of auto-transformations for the Hietarinta equation

Abstract

Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of integrable equations and autotransformations of the Hietarinta equation.