Abstract
Based on the Lie superalgebra spl(2, 1) and the TAH scheme, we generate (1+1)-dimensional and (2+1)-dimensional super soliton hierarchies associated with spl(2, 1). And by using the super-trace identity on Lie superalgebras, we construct the super-Hamiltonian structures of these new super soliton hierarchies. At last, we also obtain the Darboux transformations of the (1+1)-dimensional super soliton hierarchy.
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