Classification of five-point differential-difference equations II

TL;DR

This paper completes the classification of integrable five-point differential-difference equations using symmetry methods, identifying 14 equations including some potentially new ones, and explores their transformations and symmetries.

Contribution

It provides a comprehensive classification of integrable five-point differential-difference equations, including new equations and their transformations, advancing the understanding of their structure.

Findings

Identified 14 integrable five-point differential-difference equations.

Discovered transformations relating most equations and their symmetries.

Some equations are potentially new to the literature.

Abstract

Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201 (27pp)], of integrable autonomous five-point differential-difference equations. The resulting list, up to autonomous point transformations, contains 14 equations some of which seem to be new. We have found non-autonomous or non-point transformations relating most of the obtained equations among themselves as well as their generalized symmetries.