On some class of differential-difference equations admitting Lax representation

TL;DR

This paper identifies classes of differential-difference equations that admit Lax representations, extending known evolutionary equations and contributing to the understanding of integrable systems.

Contribution

It introduces new classes of differential-difference equations with Lax representations, generalizing existing evolutionary equations.

Findings

Identified classes of integrable differential-difference equations.

Extended the framework of known evolutionary equations.

Provided conditions for the existence of Lax representations.

Abstract

This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.