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Explorations of the Extended ncKP Hierarchy

Aristophanes Dimakis·Folkert Muller-Hoissen
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Abstract

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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Aristophanes Dimakis, Folkert Muller-Hoissen. 2004-06-16. Explorations of the Extended ncKP Hierarchy. https://doi.org/10.1088/0305-4470%2F37%2F45%2F011

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