Higher Gel'fand-Dikii structures

Details Higher Gel'fand-Dikii structures Higher Gel'fand-Dikii structures

1993-09-07

arxiv.org/abs/hep-th/9309038v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

We apply the procedure of Magri and Weinstein 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 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 structues, in terms of the Baker-Akhiezer functions. Finally we describe the symplectic leaves of these Poisson structures.

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