Explorations of the extended ncKP hierarchy
Abstract
A recently obtained extension (xncKP) of the Moyaldeformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyaldeformation 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 wellknown bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) BakerAkhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that Nsoliton 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2004
 DOI:
 10.1088/03054470/37/45/011
 arXiv:
 arXiv:hepth/0406112
 Bibcode:
 2004JPhA...3710899D
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 34 pages, correction of typos in (7.2) and (7.5)