On a direct approach to quasideterminant solutions of a noncommutative modified KP equation

TL;DR

This paper explores quasideterminant solutions to a noncommutative modified KP equation, demonstrating their derivation via Darboux transformations and establishing a link to the noncommutative KP equation through the Miura transformation.

Contribution

It introduces a direct approach to quasideterminant solutions for the noncommutative mKP equation and clarifies their relation to the noncommutative KP equation.

Findings

Solutions expressed as quasideterminants are verified directly.

Darboux transformations explain the origin of solutions.

An explicit connection between noncommutative mKP and KP equations is established.

Abstract

A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation.