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VOLUME 58 (1993) | ISSUE 8 | PAGE 677
Higher Hamiltonian structures (the sl2 case)
We apply the procedure of Magri and Weinstein to produce an mfmity of compatible Poisfon structures on a biharailtonian manifold, to the case of the KdV phase space. The higher Gel'fand-Dikii structures thus obtained contain non local terms, which we express with the help of the r.h.s. of the KdV hierarchy. We also give a generating function for all these Poisson structures, in terms of the Baker-Akhiezer functions. Finally we describe the symplectic leaves of these Poisson structures.