Bicomplex formulation and Moyal deformation of (2+1)-dimensional Fordy-Kulish systems

Abstract

Using bicomplex formalism we construct generalizations of Fordy-Kulish systems of matrix nonlinear Schroedinger equations on two-dimensional space-time in two respects. Firstly, we obtain corresponding equations in three space-time dimensions. Secondly, a Moyal deformation is applied to the space-time coordinates and the ordinary product of functions replaced by the Moyal product in a suitable way. Both generalizations preserve the existence of an infinite set of conservation laws.

13 pages, additional references, serious revision in section 5: W-equation (5.14) and its derivation was missing

References in corpus (6)

• String Theory and Noncommutative Geometry
• Anti-self-dual Yang-Mills equations on noncommutative spacetime
• Bi-differential calculi and integrable models
• Complete integrability of derivative nonlinear Schrödinger-type equations
• Bicomplexes, Integrable Models, and Noncommutative Geometry
• Bicomplexes and Integrable Models

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• Bicomplexes and Backlund transformations
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Bicomplexes and Conservation Laws in Non-Abelian Toda Models