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

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.