Integrable Matrix Modified Korteweg-de Vries Equations Derived from Reducing AKNS Lax Pairs

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.