Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-01-21
J.Phys.A37:4069-4084,2004
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, some minor changes in section 4, typos in (2.4),(3.38),(4.15) corrected, to appear in Journal of Physics A
Scientific paper
10.1088/0305-4470/37/13/010
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective `noncommutative' deformed equation.
Dimakis Aristophanes
Muller-Hoissen Folkert
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