On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits
C.X. Li, J.J.C. Nimmo, K.M. Tamizhmani
TL;DR
This paper develops quasideterminant solutions for a non-Abelian Hirota-Miwa equation and its continuum limits, leading to a hierarchy of noncommutative differential-difference equations including the noncommutative KP equation.
Contribution
It introduces quasideterminant solutions for the non-Abelian Hirota-Miwa equation and derives a hierarchy of related noncommutative equations through continuum limits.
Findings
Constructed quasideterminant solutions for the non-Abelian Hirota-Miwa equation
Derived a hierarchy of noncommutative differential-difference equations
Established solutions for the noncommutative KP equation
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.
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