Scalene Yang-Baxter maps and Lax triples
S. Konstantinou-Rizos, T. Kouloukas

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.
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