Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

Abstract

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Plücker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Plücker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared.

References in corpus (2)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Noncommutative Solitons and D-branes

Cited by in corpus (6)

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• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits
• 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
• Noncommutative Spectral Decomposition with Quasideterminant