Explorations of the Extended ncKP Hierarchy

Details Explorations of the Extended ncKP Hierarchy Explorations of the Extended ncKP Hierarchy

2004-06-13

arxiv.org/abs/hep-th/0406112v2

J.Phys. A37 (2004) 10899-10930

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, correction of typos in (7.2) and (7.5)

Scientific paper

10.1088/0305-4470/37/45/011

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.

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