Set-theoretic Yang-Baxter equation and related integrable maps

Set-theoretic Yang-Baxter equation and related integrable maps

Dr George Papamikos

We study some solutions of the set-theoretic parametric Yang-Baxter equation. These solutions are bi-rational maps with several invariants and a Lax representation [1]. We show that we can use these maps as building blocks in order to construct higher dimensional bi-rational maps which have nice properties and we prove their integrability in the Liouville sense. These maps can be seen as higher dimensional generalisations of the famous integrable QRT maps [2], known as Adler's Triad maps [3]. Finally, we discuss some new generalisations [4].

References

[1] A. P. Veselov, Yang-Baxter maps and integrable dynamics, Physics Letters A 314 (2003), 214 - 221. 
[2] G. R. W. Quispel, J. A. G. Roberts, C. J. Thompson, Integrable mappings and soliton equaions II, Physica D: Nonlinear Phenomena 34 (1989), 183-192.
[3] S. Konstantinou-Rizos, G.Papamikos, Entwining Yang-Baxter maps related to NLS type equations, arXiv:1907.00019
[4] V. E. Adler, On a class of third order mappings with two rational invariants, preprint, arXiv:nlin/0606056v1.

Speaker

Dr George Papamikos is a Research Fellow in the School of Mathematics, University of Leeds.