NEW SUPERSYMMETRIZATIONS OF THE GENERALIZED KDV HIERARCHIES

Recently we investigated a new supersymmetrization procedure for the K dV hierarchy inspired in some recent work on supersymmetric matrix mod els. We extend this procedure here for the generalized KdV hierarchies . The resulting supersymmetric hierarchies are generically nonlocal, e xcept for the case of Boussinesque which we treat in detail. The resul ting supersymmetric hierarchy is integrable and bi-Hamiltonian and con tains the Boussinesque hierarchy as a subhierarchy. In a particular re alization, we extend it by defining supersymmetric odd flows. We end w ith some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy.