THE HAMILTONIAN-STRUCTURE OF THE N=2 SUPERSYMMETRIC GNLS HIERARCHY

The first two Hamiltonian structures and the recursion operator connec ting all evolution systems and Hamiltonian structures of the N = 2 sup ersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 su perfields in two different superfield bases with local evolution equat ions. Their bosonic limits are studied in detail. New local and nonloc al bosonic and fermionic integrals both for the N = 2 supersymmetric ( n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an e xample, in the n = 1, m = 1 case, the algebra and the symmetry transfo rmations for some of them are worked out and a rich N = 4 supersymmetr y structure is uncovered. (C) 1997 Elsevier Science B.V.