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

2007/01/13 by C. R. Gilson, Gilson, C. R., J. J. C. Nimmo +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0701027

11 pages

openalex publication_date 2007/01/13 · arxiv created 2007/01/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Quasi-Pfaffians and applications
• Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
• Tau functions of the constrained matrix KP hierarchy
• The noncommutative KP hierarchy and its solution via descent algebra
• Darboux transformations and related non-Abelian integrable differential-difference systems of the derivative nonlinear Schrödinger type

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