2016/08/13 by Jean-Pierre Magnot, Magnot, Jean-Pierre, Enríque G. Reyes +1 · 3 citations
Mathematics · Physics and Astronomy · #35Q51 #37K10 #37K25 #37K30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1608.03994
openalex publication_date 2016/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We recall the notions of Fr "olicher and diffeological spaces and we build\nregular Fr "olicher Lie groups and Lie algebras of formal pseudo-differential\noperators in one independent variable. Combining these constructions with a\nsmooth version of the Mulase factorization of infinite dimensional groups based\non formal pseudo-differential operators, we present two proofs of the\nwell-posedness of the Cauchy problem for the Kadomtsev-Petviashvili (KP)\nhierarchy in a smooth category. We also generalize these results to a KP\nhierarchy modelled on formal pseudo-differential operators with coefficients\nwhich are series in formal parameters, describe a rigorous derivation of the\nHamiltonian interpretation of the KP hierarchy, and discuss how solutions\ndepending on formal parameters can lead to sequences of functions converging to\na class of solutions of the standard KP-I equation.\n