On construction of discrete Darboux integrable equations

TL;DR

This paper explores the discretization of Darboux integrable equations, introducing a method based on characteristic algebras to generate new integrable discrete equations from continuous ones.

Contribution

It presents a novel approach to discretize Darboux integrable equations using characteristic algebras, resulting in new examples of integrable discrete equations.

Findings

New integrable discrete equations constructed

Discretization method based on characteristic algebras

Enhanced understanding of Darboux integrability in discrete systems

Abstract

The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation. In the present paper, the discretization of the differential-discrete equations is done using the corresponding characteristic algebras. New examples of integrable discrete equations are obtained.