Sotiris Konstantinou-Rizos “Integrable Systems, Darboux Transformations and Yang-Baxter maps“

7 ноября 2023 Our next speaker will be Sotiris Konstantinou-Rizos from Yaroslavl State University. Title: Integrable Systems, Darboux Transformations and Yang-Baxter maps Abstract: Darboux and Baecklund transformations are very important tools in the theory of Integrable Systems. On one hand they can be used to construct interesting solutions to integrable nonlinear PDEs starting from trivial ones, and on the other hand they constitute a bridge between integrable PDEs and integrable PΔEs. At the same time, the Yang-Baxter equation is one of the most fundamental equations of mathematical physics, and it has applications in a very wide range of fields of Mathematics and Physics; from geometry and representation theory, to statistical and quantum mechanics. In this talk, I will present several Darboux transformations of NLS type and I will explain what integrable discretisation of PDEs via Darboux-Baecklund transforms means. Then, I will demonstrate the relation between discrete integrable systems and Yang-Baxter maps and will show how to use Darboux matrices for constructing Yang-Baxter maps. I will show commutative and noncommutative (on division rings) examples of Yang-Baxter maps of KdV, NLS and derivative NLS type. This talk is based on some old results in collaboration with A.V. Mikhailov and P. Xenitidis and some new results with P. Xenitidis, X. Fisenko and A. Nikitina.