Two Distinct Group Reductions Leading to Integrable Coupled mKdV Models

Abstract We aim to explore pairs of distinct group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problem that lead to integrable coupled modified Korteweg–de Vries (mKdV) models. Specifically, we formulate three representative group reduction schemes, each resulting in the derivation of new integrable coupled mKdV systems. This analysis not only introduces novel examples of integrable models but also provides fresh insights into the classification of third-order integrable equations.