On a direct approach to quasideterminant solutions of a noncommutative KP equation

Details On a direct approach to quasideterminant solutions of a noncommutative KP equation On a direct approach to quasideterminant solutions of a noncommutative KP equation

2007-01-13

arxiv.org/abs/nlin/0701027v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.

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