On the discretization of Darboux Integrable Systems admitting the second-order integrals

TL;DR

This paper explores the discretization of Darboux integrable systems using their integrals, resulting in new semi-discrete examples that preserve integrability properties.

Contribution

It introduces a novel discretization approach based on x- and y-integrals, producing new semi-discrete Darboux integrable systems.

Findings

New semi-discrete Darboux integrable systems identified

Discretization preserves integrability properties

Method based on x- and y-integrals

Abstract

We study discretization of Darboux integrable systems. The discretization is done by using $x$- or $y$-integrals of the considered systems. New examples of semi-discrete Darboux integrable systems are obtained.