Noncommutative deformation of the Kadomtsev-Petviashvili hierarchy
type: Item
instance of: scholarly article
title: Noncommutative deformation of the Kadomtsev-Petviashvili hierarchy
zbMATH Open document ID: 0921.35146
DOI: 10.1007/BF02365314
author: E. E. Demidov
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-10-22T00:00:00Z
review text: The paper proposes a generalization of the Kadomtsev-Petviashvili hierarchy of exactly integrable PDEs to the case of a noncommutative space-time, in the spirit of the quantum group theory. The main objective of the work is to prove the existence and uniqueness for the corresponding noncommutative analog of the so-called Sato-Wilson equation. To this end, a differential calculus is built on the noncommutative space-time, and an algebra of pseudodifferential operators, related to the skew differentiation, is described, which allows to prove the completeness integrability theorem for the noncommutative Sato-Wilson equation.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 46L85
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1213205
zbMATH Keywords: supersymmetry
zbMATH Keywords: integrability
zbMATH Keywords: Kadomtsev-Petviashvili hierarchy
zbMATH Keywords: noncommutative space-time
zbMATH Keywords: noncommutative Sato-Wilson equation
reviewed by: B. A. Malomed
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1213205