Abstract
Based on the Lie superalgebras osp(2|2) and spo(2|2), we generate some new super soliton hierarchies. These hierarchies can reduce to the AKNS hierarchy and the super-AKNS hierarchy. And by using the supertrace identity on Lie superalgebras, we construct the super-Hamiltonian structures of these new super soliton hierarchies. Then, as the applications of spo(2|2) ≅ osp(2|2) and spo(2|2) ≅ sl(1|2), we obtain the relations of different hierarchies associated with different Lie superalgebras.
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