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

**Konstantinou-Rizos, S ***(University of Leeds)*

Tuesday 09 July 2013, 11:00-11:30

Seminar Room 1, Newton Institute

#### Abstract

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.

#### Presentation

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