SEMINAIRE Mulhousien de MATHEMATIQUES

résumé/abstract


Folkert Müller-Hoissen (MPI, Göttingen)

Bidifferential graded algebras and soliton equations

 

A bidifferential graded algebra (or bidifferential calculus) is a graded differential algebra with respect to two different antiderivations which anticommute. Many integrable systems can be expressed in terms of this structure, which generalizes in particular the structure underlying the self-dual Yang-Mills equations, but moreover covers e.g. the Kadomtsev-Petviashvili equation and its hierarchy, and also discrete integrable equations. Within this framework one can establish various solution generating techniques in a simple and universal way. As an application, we derive soliton-like solutions of some integrable equations with nontrivial interaction. The framework extends towards noncommutative geometry. All this is based on joint work with A. Dimakis.

 


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Dernières modifications / Last modifications :  21 Mai 2008