Reducing Lax pairs to obtain integrable matrix modified Korteweg–de Vries models

Abstract

This paper explores the matrix modified Korteweg–de Vries (mKdV) integrable models using similarity transformations. The study employs the Lax pair formulation as a foundation, proposing pairs of similarity transformations to reduce the Lax pairs of the Ablowitz–Kaup–Newell–Segur matrix spectral problems, thereby deriving integrable matrix mKdV models. Four illustrative scenarios are discussed to present specific examples of these reduced integrable models.