A higher-dimensional multi-component integrable hierarchy and its integrable couplings

By use of a (2 + 1)-dimensional zero-curvature equation and Tu scheme, a (2 + 1)-dimensional multi-component integrable hierarchy is obtained. As reduction cases, the (2 + 1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and Kaup–Newell (KN) hierarchy are engendered, respectively. Taking advantage of the expanding loop algebra F∼M of the loop algebra G∼M, a type of expanding Lax integrable model of the above-mentioned (2 + 1)-dimensional multi-component integrable hierarchy, i.e. integrable couplings, is worked out.