The exact solutions for the nonisospectral AKNS hierarchy through the inverse scattering transform

Exact solutions for the nonisospectral AKNS hierarchy are obtained through the inverse scattering transform. Some explicit forms of these solutions are further given. Reductions are also considered. Exact solutions of some nonisospectral hierarchies, such as the nonisospectral mKdV hierarchy, the nonisospectral KdV hierarchy, the nonisospectral nonlinear Schrödinger hierarchy and the nonisospectral sine-Gordon hierarchy, are obtained.