The Cauchy problem of the Kadomtsev-Petviashvili hierarchy with arbitrary coefficient algebra. (21st December 2017)

• Record Type: Journal Article
• Authors: Rad, Anahita Eslami; Magnot, Jean-Pierre; Reyes, Enrique G.
• Is Part Of: Journal of nonlinear mathematical physics. Volume 24(2017)Supplement 1
• Page Start: 103
• Page End: 120
• Publication Date: 2017-12-21
• Subjects: Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2017.1418057
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : Mulase solved the Cauchy problem of the Kadomtsev-Petviashvili (KP) hierarchy in an algebraic category in "Solvability of the super KP equation and a generalization of the Birkhoff decomposition" ( Inventiones Mathematicae, 1988), making use of a delicate factorization of an infinite-dimensional group of formal pseudodifferential operators of infinite order. We prove Mulase's factorization theorem in a smooth category in the setting of formal pseudo-differential operators with coefficients in a (non-commutative) algebra equipped with a valuation. As an application, we solve the initial value problem for the KP hierarchy using r -matrix theory.