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

References in corpus (4)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation
• Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
• Noncommutative Solitons and D-branes

Cited by in corpus (1)

• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations