Abstract
•Based on a Lie super-algebra B(0,1), a new generalized super AKNS hierarchy is introduced.•By making use of the super-trace identity, the obtained generalized super AKNS hierarchy can be written as the super bi-Hamiltonian formulation.•A generalized super AKNS hierarchy with self-consistent sources is also derived by making use of the variational derivative.
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.