A novel kind of reduced integrable matrix mKdV equations and their binary Darboux transformations

Abstract

A novel kind of reduced integrable matrix mKdV equations is generated from a group reduction replacing the spectral parameter [Formula: see text] with [Formula: see text] in the matrix AKNS spectral problems. The traditional replacement in making integrable reductions is to replace the spectral parameter [Formula: see text] with its complex conjugate [Formula: see text]. Binary Darboux transformations are constructed by use of Lax pairs and adjoint Lax pairs, and thus, soliton solutions are presented for the resulting reduced integrable matrix mKdV equations from the zero seed solution.