A (2Â +Â 1)-dimensional multi-component AKNS integrable hierarchy and its expanding model

A set of multi-component matrix Lie algebra is constructed, it follows a type of new loop algebra that is presented. A (2 + 1)-dimensional multi-component AKNS integrable hierarchy is obtained by using a (2 + 1)-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system is worked out.