Families of Integrable Equations

TL;DR

This paper introduces a method to generate families of lattice equations, demonstrating that these families, connected through Bäcklund transformations, inherit integrability properties from their integrable members.

Contribution

The authors develop a novel approach to construct families of lattice equations with multiple parameters, highlighting the inheritance of integrability within these families.

Findings

Two families of lattice equations with three parameters each are constructed.

Members of each family are interconnected via Bäcklund transformations.

At least one member of each family is proven to be integrable.

Abstract

We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some integrability properties.