Séminaire de Géométrie et Quantification


Joseph Krasil'shchik
(Moscou)


Non-local geometry of PDE’s and Integrability


Lundi 23 janvier à 16h45, IHP salle
01,

Résumé : Integrability of PDEs is linked to the existence of certain operators, such as recursion, symplectic and Hamiltonian operators, which are related to the nonlocal geometry of equations (differential coverings) in two different ways. First, in many cases (and practically always for recursion operators) they contain nonlocal terms, such as D_x^{ −1} , or more complicated terms. Secondly, their geometric definition rests on the construction of two special and natural coverings, the tangent and cotangent ones. I shall present an overview of the theory of differential coverings over infinitely prolonged PDEs and of their role in the study of integrable systems.

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