Abstract
Introducing squared eigenfunctions in the Moyal-deformed Lax equations generates an extended noncommutative KP (ncKP) hierarchy. The compatibility equations between the ncKP flows and the extended ncKP flows and the compatibility equations among the extended ncKP flows themselves are constructed. The n-reductions and the k-constraints are analyzed, and thus, the ncKP hierarchy with self-consistent sources, the constrained ncKP hierarchy, and the constrained ncKP hierarchy with self-consistent sources are presented. Various illustrative examples are worked out, together with their Lax representations involving pseudodifferential Lax operators. (C) 2010 American Institute of Physics. [doi:10.1063/1.3458580]