On a direct approach to quasideterminant solutions of a noncommutative KP equation
QC | Nonlinear Sciences - Exactly Solvable and Integrable Systems
arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems
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.