Higher Gel'fand-Dikii structures
High Energy Physics - Theory
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9309038,
title = {Higher Gel'fand-Dikii structures},
author = {B. Enriquez and A. Orlov and V. Rubtsov},
journal= {arXiv preprint arXiv:hep-th/9309038},
year = {2007}
}