Dual similarity transformations and integrable reductions of matrix mKdV models

Abstract

This work aims to construct dual similarity transformations and explore integrable reductions of matrix modified Korteweg–de Vries (mKdV) models. Starting from the zero-curvature formulation, the study employs similarity transformations as the principal tool. Four representative scenarios of reduced Ablowitz–Kaup–Newell–Segur matrix spectral problems are analyzed, providing concrete examples of reduced matrix mKdV integrable models derived through dual similarity transformations.