Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation

Abstract

In this paper, we present Lax pairs and solutions for a nonsymmetric lattice equation, which is a torqued version of the lattice potential Korteweg-de Vries equation. This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations. Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using Bäcklund transformations.