Abstract. This paper aims to reduce Lax pairs of AKNS matrix spectral problems using pairs of group reductions or similarity transformations. The corresponding modified Korteweg-de Vries matrix integrable hierarchies are obtained from the reduced Lax pairs, amending the standard AKNS integrable hierarchies. A few exemplary cases are analyzed and computed to demonstrate the diversity of modified Korteweg-de Vries matrix integrable equations.

Key words: AKNS Lax pair, Matrix spectral problem, Zero-curvature equation, Soliton hierarchy.