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Explorations of the Extended ncKP Hierarchy | | Aristophanes Dimakis
; Folkert Muller-Hoissen
; | | Date: |
13 Jun 2004 | | Journal: | J.Phys. A37 (2004) 10899-10930 | | Subject: | High Energy Physics - Theory; Mathematical Physics; Exactly Solvable and Integrable Systems | hep-th math-ph math.MP nlin.SI | | 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. | | Source: | arXiv, hep-th/0406112 | | Services: | Forum | Review | PDF | Favorites | |
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