Discretization of hyperbolic type Darboux integrable equations preserving integrability

TL;DR

This paper introduces a new method for discretizing hyperbolic Darboux integrable equations that preserves their integrability, providing new discrete models of Liouville type equations.

Contribution

It proposes a novel integrable discretization approach based on integrals, with new discrete Liouville type models demonstrated.

Findings

New integrable discretization method for Darboux equations

Presentation of new discrete Liouville models

Preservation of integrability in discretization

Abstract

A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.