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