From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations
arXiv:2504.21094
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 Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang--Baxter maps are completely integrable.
14 pages. Accepted for publication in Theoretical and Mathematical Physics