A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

摘要

For the orthosymplectic Lie superalgebra OSP(2, 2), we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.