Real Reduced Matrix mKdV Integrable Hierarchies Under Two Local Group Reductions

We propose a kind of reduced Ablowitz-Kaup-Newell-Segur matrix spectral problems under two local group reductions by similarity transformations. Associated integrable hierarchies of matrix mKdV type integrable models are presented, which amend the complex matrix mKdV integrable hierarchies. Zero curvature equations are key objects in generating integrable models.