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Integrable two-component systems of difference equations

Pavlos Kassotakis
Monday, February 7, 2022 - 16:00 to 17:00

We will present two lists of two-component systems of integrable difference equations defined on the edges of the $\mathbb{Z}^2$ graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatibility of these systems. Imposing constraints consistent with the systems of difference equations, we recover known integrable quad-equations including the discrete version of the Krichever-Novikov equation. The systems of difference equations give us, in turn, Yang-Baxter maps. Some of these maps can be considered as particular reductions of non-abelian Yang-Baxter maps.

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