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