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Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups

Abstract : We recall the notions of Frolicher and diffeological spaces, and we build regular Frolicher Lie groups and Lie algebras of formal pseudo-differential operators in one independent variable. Combining these constructions with a smooth version of Mulase's deep algebraic factorization of infinite-dimensional groups based on formal pseudo-differential operators, we present two proofs of the well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili (KP) hierarchy in a smooth category. We also generalize these results to a KP hierarchy modelled on formal pseudo-differential operators with coefficients which are series in formal parameters, we describe a rigorous derivation of the Hamiltonian interpretation of the KP hierarchy, and we discuss how solutions depending on formal parameters can lead to sequences of functions converging to a class of solutions of the standard KP-II equation.
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https://hal.archives-ouvertes.fr/hal-02497053
Contributor : Jean-Pierre Magnot Connect in order to contact the contributor
Submitted on : Tuesday, March 3, 2020 - 2:25:09 PM
Last modification on : Wednesday, November 3, 2021 - 9:18:32 AM

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Jean-Pierre Magnot, Enrique G. Reyes. Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups. Annales Henri Poincaré, Springer Verlag, 2020, 21 (6), pp.1893-1945. ⟨10.1007/s00023-020-00896-3⟩. ⟨hal-02497053⟩

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