Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-01-12
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, Plain TeX. Some statements more precisely rephrased; expanded reference list
Scientific paper
10.1016/0370-2693(95)00357-Q
Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.
Mas Javier
Ramos Eduardo
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