Darboux transformations with tetrahedral reduction group and related integrable systems

TL;DR

This paper develops new integrable differential and difference systems using Darboux transformations linked to a tetrahedral reduction group, expanding the understanding of automorphic Lie algebra-based integrable models.

Contribution

It introduces novel two-component integrable systems derived from an ${rak{sl}}_3({f C})$ automorphic Lie algebra using a Lax-Darboux scheme, demonstrating their integrability.

Findings

New two-component integrable systems derived from automorphic Lie algebra.

Proof of integrability via Lax pairs and symmetries.

Application of Darboux transformations with tetrahedral reduction group.

Abstract

In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfrak{sl}}_3({\mathbb{C}})$-based automorphic Lie algebra. The integrability of the found systems is demonstrated via Lax pairs and generalised symmetries.