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

Abstract

A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation.

References in corpus (3)

• An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions
• Factorization methods for Noncommutative KP and Toda hierarchy
• Explorations of the Extended ncKP Hierarchy

Cited by in corpus (25)

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• Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations
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• Quasideterminant solutions of the generalized Heisenberg magnet model
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• Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation
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• Noncommutative Solitons and Quasideterminants
• Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
• Soliton Scattering in Noncommutative Spaces
• Quasideterminant solutions of NC Painlevé II equation with the Toda solution at $n=1$ as a seed solution in its Darboux transformation
• Explicit Flow Equations and Recursion Operator of the ncKP hierarchy
• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields
• Solitons in Open N=2 String Theory
• A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system
• Darboux Transformation for the Hirota equation
• Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model
• Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy