A LIE SUPERALGEBRA AND CORRESPONDING HIERARCHY OF EVOLUTION EQUATIONS

A Lie super algebra G is constructed and an isospectral problem with five potentials is designed. From there, a corresponding hierarchy of nonlinear evolution equations is derived and super-AKNS, super-TD, super-D-AKNS are deduced. Their super-Hamiltonian structure is established by making use of the supertrace identity, and they are intergrable in sense of Liouville.