N = 2 KP AND KDV HIERARCHIES IN EXTENDED SUPERSPACE

We give the formulation in extended superspace of an N = 2 supersymmet ric KP hierarchy using chirality preserving pseudo-differential operat ors. We obtain two quadratic hamiltonian structures, which lead to dif ferent reductions of the KP hierarchy. In particular we find two diffe rent hierarchies with the N = 2 classical super-W-n, algebra as a hami ltonian structure. The relation with the formulation in N = 1 superspa ce and the bosonic limit are carried out.