Set theoretical reflection equation: origin and applications to discrete integrable systems

Vincent Craudrelier (City University London)

Tuesday 5th November, 2013 15:00-16:00 Maths 203

Abstract

We will present results on the vector nonlinear Schrödinger equation on the half line. Special attention to the question of factorisation of soliton interactions led to the discovery of the set theoretical reflection equation. The latter is a companion equation to the set theoretical Yang-Baxter equation which plays an important role in the theory of integrable equations on quad-graphs. After reviewing this connection, we will present the new features that the set theoretical reflection equation brings into the game, in particular the notion of three dimensional boundary consistency.

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