New simple method for obtaining integrable hierarchies of soliton equations with multicomponent potential functions

A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra (G) over tilde (M) is constructed, whose commutation operation is clear as that in loop algebra (A) over tilde (1). Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra (F) over tilde (M) of the loop algebra (G) over tilde is constructed. Taking advantage of (F) over tilde (M) above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out.