Binary Darboux transformation for general matrix mKdV equations and reduced counterparts

Abstract

Based on Lax pairs and adjoint Lax pairs, a Darboux transformation is constructed for a class of general matrix mKdV equations and a kind of symmetric integrable reductions of the general case is analyzed. A fundamental step is to formulate a new type of Darboux matrices, in which eigenvalues could be equal to adjoint eigenvalues. From the zero seed solution, the resulting binary Darboux transformation is used to generate soliton solutions for the general matrix mKdV equations and the corresponding reduced counterparts.