Seminar talk, 23 November 2022

From Geometry of Differential Equations
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Speaker: Jean-Pierre Magnot

Title: New perspectives for generalized Kadomtsev-Petviashvili hierarchies

In the setting of diffeological differential algebras, we first expose step by step how the classical algebraic construction of the solution of the (classical) Kadomtsev-Petviashvili hierarchy can be extended in order to get well-posedness for Kadomtsev-Petviashvili hierarchies in this generalized setting. Of course, we give a short exposition of the necessary notions in diffeologies for non-specialists of this topic.

Then, we discuss the Hamiltonian formulation in a refreshed way. Finally, we deduce the corresponding Kadomtsev-Petviashvili equations, first in an abstract formulation, and in a series of examples.

Slides: beamer-krasilshchik-2022.pdf

arXiv:2101.04523, Mi tmf10046