The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N=2 supersymmetric (n,m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n=1, m=1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N=4 supersymmetry structure is uncovered.