On the integrability of a discrete analogue of the Kaup-Kupershmidt equation

TL;DR

This paper introduces a new discrete equation related to the Kaup-Kupershmidt equation, proves its integrability through L-A pairs and conservation laws, and suggests a novel method for deriving conservation laws.

Contribution

It presents a new integrable discrete analogue of the Kaup-Kupershmidt equation and a novel scheme for deriving conservation laws from L-A pairs.

Findings

The discrete equation reduces to the Kaup-Kupershmidt equation in the continuous limit.

The integrability of the discrete equation is established via L-A pairs and conservation laws.

A new method for deriving conservation laws from L-A pairs is proposed.

Abstract

We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimensional lattice. We have established that in the continuous limit this new equation goes into the well-known Kaup-Kupershmidt equation. We have also proved its integrability by constructing an $L-A$ pair and conservation laws. Moreover, we present a possibly new scheme for deriving conservation laws from $L-A$ pairs.