Darboux and binary Darboux transformations for discrete integrable systems--Discrete potential KdV equation

Ying Shi (University of Glasgow)

Tuesday 19th November, 2013 15:00-16:00 Maths 203


The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the  discrete potential KP equation.  For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form.  We discuss reductions of both systems to the discrete KdV and discrete potential KdV equations, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations.

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