A family of expanding integrable models of AKNS hierarchy of equations

First of all, a new subalgebra of loop algebra (A) over tilde (2) is constructed. Designing an isospectral problem and using Tu-model we obtain a family of expanding integrable models of the well-known AKNS hierarchy of equations, i.e. integrable couplings. Then the generalized form of the method for obtaining integrable couplings is established. It follows that the integrable couplings for a large kinds of hierarchies of equations, such as KN hierarchy, GJ hierarchy, WKI hierarchy etc, admit this approach. Therefore, the method proposed in this paper has practical values. Finally, as special cases, the integrable couplings of KdV equation and MKdV equation are obtained.