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Darboux transformations and Yang–Baxter maps

Wednesday, 17 November 2021 , 3.30pm

Dr Sotiris Konstantinou-Rizos Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Russia.

In this talk, I will make an introduction to the theory of Yang–Baxter maps, namely settheoretical solutions to the quantum Yang–Baxter equation. I will explain the relation between Yang–Baxter maps and equations on quad-graphs, as well as the association of such maps with matrix refactorisation problems.

Moreover, I will show a method to construct such maps using Darboux transformations. I will present some results on commutative and noncommutative Yang–Baxter maps of Nonlinear Schrödinger type. This work is supported by the Russian Science Foundation (grant No. 20-71-10110).


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