Noncommutative AKNS Equation Hierarchy and Its Integrable Couplings with Kronecker Product

We present a noncommutative version of the Ablowitz--Kaup--Newell--Segur (AKNS) equation hierarchy, which possesses the zero curvature representation. Furthermore, we derive the noncommutative AKNS equation from the noncommutative (anti-)self-dual Yang--Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, the
integrable coupling system of the noncommutative AKNS equation hierarchy is constructed by using the Kronecker product.