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VOLUME 58 (1993) | ISSUE 8 | PAGE 677
Higher Hamiltonian structures (the sI2 case)
The procedure of Magri and Weinstein is applied to produce an infinity of compatible Poisson structures on a bihamiltonian manifold, to the case of the KdV phase space. The higher Gel'fand-Dikii structures thus obtained contain nonlocal terms which are expressed with the help of the r.h.s. of the KdV hierarchy. A generating function for all these Poisson structures is given in terms of the Baker-Akhiezer functions. The symplectic leaves of these Poisson structures are described.