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Darboux transformations, discrete integrable systems and related Yang-Baxter maps

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In this talk we derive Darboux transformations which are invariant under the action of finite reduction groups. We present Darboux transformations for the NLS equation, the derivative NLS equation and a deformation of the derivative NLS equation. We use the associated Darboux matrices to define discrete Lax pairs and derive discrete integrable systems. Moreover, we use these Darboux matrices to construct 6-dimensional Yang-Baxter maps which can be restricted to 4-dimensional YB maps on invariant leaves. The former are completely integrable discrete maps.

This talk is part of the Isaac Newton Institute Seminar Series series.

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