2005/03/28 by Alexander Zheglov, Zheglov, Alexander
Mathematics · Physics and Astronomy · #35A27 #35Q53 #37K10 #58F07 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35A27 #msc:35Q53 #msc:37K10 #msc:58F07
paper · pdf · doi:10.48550/arxiv.math-ph/0503067
43 pages, revised version with corrected typos
arxiv created 2005/11/07 · arxiv updated 2009/12/01
In this paper we introduce new various generalizations of the classical Kadomtsev-Petviashvili hierarchy in the case of operators in several variables. These generalizations are the candidates for systems that should play the role, analogous to the role of the KP hierarchy in the classical KP theory, in a generalized KP theory. In particular, they should describe flows of some generalized geometric datas, including those described by A.N.Parshin, for certain initial conditions. The unique solvability of the initial value problem for the generalized KP hierarchies is established. The connection of these systems with universal families of isospectral deformations of certain pairs of commuting differential operators is opened. To prove the solvability of the systems we generalize several results from the works of M.Mulase and A.N.Parshin.