Grassmann extensions of discrete Integrable Systems and their associated Yang-Baxter maps

Speaker: Sotiris Konstantinou-Rizos, Yaroslavl State University

Yang-Baxter maps and equations on quad-graphs are two sides of the same coin.

In this talk, I shall present a simple scheme for constructing Grassmann extensions of Yang-Baxter maps (namely, set-theoretical solutions of the Yang-Baxter equation) together with their associated discrete integrable systems. As an application, we construct a Grassmann extension of a Yang-Baxter map related to the discrete potential KdV equation that can be squeezed down to a novel, noncommutative system of lattice equations. The latter system is integrable, and its bosonic limit is the discrete potential KdV equation. Furthermore, we will also be discussing the 3D-consistency of the obtained systems.

This event is free to attend.