Reductions and degenerate limits of Yang-Baxter maps with 3× 3 Lax matrices

2025/01/02 by Adamopoulou, P., Kouloukas, T. E., Papamikos, G. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2501.01210

Abstract

We generalise a family of quadrirational parametric Yang-Baxter maps with 3× 3 Lax matrices by introducing additional essential parameters. These maps preserve a prescribed Poisson structure which originates from the Sklyanin bracket. We investigate various low-dimensional reductions of this family, as well as degenerate limits with respect to the parameters that were introduced. As a result, we derive several birational Yang-Baxter maps, and we discuss some of their integrability properties. This work is part of a more general classification of Yang-Baxter maps admitting a strong 3× 3 Lax matrix with a linear dependence on the spectral parameter.

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