An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation

Abstract

Based on a Lie super-algebra B(0, 1), an integrable generalization of the super AKNS iso-spectral problem is introduced and its corresponding generalized super AKNS hierarchy is generated. By making use of the super-trace identity (or the super variational identity), the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. A generalized super AKNS soliton hierarchy with self-consistent sources is also presented.