N=2 KP and KdV hierarchies in extended superspace

Abstract

We give the formulation in extended superspace of an $N=2$ supersymmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which lead to different reductions of the KP hierarchy. In particular we find two different hierarchies with the $N=2$ classical super-${\mathcal{W}}_n$ algebra as a hamiltonian structure. The relation with the formulation in $N=1$ superspace is carried out.

18 pages, LaTeX file, important reference added

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