Bi-Hamiltonian Sturcture of Super KP Hierarchy

Abstract

We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\hat{I}›=\hat{I}{¸}^2+{\sum }_{i=-2}^{\infty }{U}_i\hat{I}{¸}^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super $W$-algebra incorporating all known extended superconformal $W_N$ algebras by reduction. We also construct the super BKP hierarchy by imposing a set of anti-self-dual constraints on the super KP hierarchy.

20 pages