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arXiv · 1608.03994

Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Fr\"olicher Lie groups

Jean-Pierre Magnot·Enrique G. Reyes
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Abstract

We recall the notions of Fr\"olicher and diffeological spaces and we build regular Fr\"olicher Lie groups and Lie algebras of formal pseudo-differential operators in one independent variable. Combining these constructions with a smooth version of the Mulase 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, describe a rigorous derivation of the Hamiltonian interpretation of the KP hierarchy, and discuss how solutions depending on formal parameters can lead to sequences of functions converging to a class of solutions of the standard KP-I equation.

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Jean-Pierre Magnot, Enrique G. Reyes. 2016-08-13. Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Fr\"olicher Lie groups. https://arxiv.org/abs/1608.03994

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