On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits

Abstract

In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the noncommutative KP equation. For each of these systems the quasideterminant solutions are constructed as well.

9 pages, 1 figure

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Cited by in corpus (9)

• Integrable properties of the differential-difference Kadomtsev-Petviashvili hierarchy and continuum limits
• Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
• Noncommutative Solitons and Quasideterminants
• Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Non-commutative Hermite--Padé approximation and integrability
• Soliton Scattering in Noncommutative Spaces
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
• A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system
• Quasideterminant solutions to a noncommutative $q$-difference two-dimensional Toda lattice equation