Scalene Yang-Baxter maps and Lax triples

TL;DR

This paper introduces scalene Yang-Baxter maps, explores their connection to matrix refactorisation, and constructs specific maps linked to integrable KdV and NLS equations.

Contribution

It generalizes the set-theoretic Yang-Baxter equation by defining scalene maps and links them to integrable systems like KdV and NLS.

Findings

Defined scalene Yang-Baxter maps and their properties.

Connected solutions to matrix refactorisation problems.

Constructed maps associated with KdV and NLS integrable equations.

Abstract

We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang-Baxter maps. Moreover, we construct scalene Yang-Baxter maps associated with integrable equations of KdV and NLS type.