A class of extended Lie superalgebras and their applications

We construct a class of extended Lie superalgebras, including a generalized Lie superalgebra B(0,1), a gener-alized Lie superalgebra spl(2,1), a generalized Lie superalgebra spo(2,2), and a generalized Lie superalgebra osp(2,2). Considering the applications of these Lie superalgebras, we obtain three different nonisospectral super AKNS hierarchies. It follows that many classical and new equations are deduced by discussing some reductions of these hierarchies, such as the nonlinear Schrodinger (NLS) equation, the Burgers equation, the heat equation, the Fokker-Planck equation, the KdV equation, and so on. Based on the Killing form on these extended Lie superalgebras, we obtain the super Hamiltonian structures of these three nonisospectral super AKNS hierarchies.