Constructing variable coefficient nonlinear integrable coupling super AKNS hierarchy and its self-consistent sources

Constructing variable coefficient super integrable equation hierarchy is an important problem in soliton theory. In this letter, new Lax pairs with some arbitrary functions are proposed and a variable coefficient integrable coupling of super AKNS hierarchy is generated. The super Hamiltonian structures of variable coefficient coupling equation hierarchy is derived with the aid of the super trace identity. Furthermore, the self-consistent sources of variable coefficient super integrable coupling hierarchy are established. It is indicated that this method is an efficient way to construct the variable coefficient super integrable equation hierarchy.