On the integrability of a lattice equation with two continuum limits

TL;DR

This paper investigates a lattice equation with two continuum limits, demonstrating its integrability through the construction of an L-A pair and conservation laws, linking it to well-known fifth-order PDEs.

Contribution

It introduces a new lattice equation with dual continuum limits and proves its integrability by explicit construction of L-A pair and conservation laws.

Findings

The lattice equation has two different continuum limits: Sawada-Kotera and Kaup-Kupershmidt equations.

The integrability of the equation is confirmed via L-A pair construction.

Hierarchy of conservation laws is established for the equation.

Abstract

We study a new example of lattice equation being one of the key equations of a recent generalized symmetry classification of five-point differential-difference equations. This equation has two different continuum limits which are the well-known fifth order partial-differential equations, namely, the Sawada-Kotera and Kaup-Kupershmidt equations. We justify its integrability by constructing an $L-A$ pair and a hierarchy of conservation laws.