From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations
Exactly Solvable and Integrable Systems
2025-05-01 v1 Mathematical Physics
math.MP
Abstract
We present a method for constructing hierarchies of solutions to -simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex equations which are related to the Adler map and Nonlinear Schr\"odinger (NLS) type equations. Moreover, we prove that some of the derived Yang--Baxter maps are completely integrable.
Cite
@article{arxiv.2504.21094,
title = {From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations},
author = {Sotiris Konstantinou-Rizos},
journal= {arXiv preprint arXiv:2504.21094},
year = {2025}
}
Comments
14 pages. Accepted for publication in Theoretical and Mathematical Physics