v 1 1 0 Ju n 20 05 CLASSICAL r - MATRICES AND COMPATIBLE POISSON STRUCTURES FOR LAX EQUATIONS ON POISSON ALGEBRAS
نویسنده
چکیده
Given a classical r-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.
منابع مشابه
Compatible Poisson-Lie structures on the loop group of SL2.
Compatible Poisson-Lie structures on the loop group of SL 2. Abstract. We define a 1-parameter family of r-matrices on the loop algebra of sl 2 , defining compatible Poisson structures on the associated loop group, which degenerate into the rational and trigonometric structures, and study the Manin triples associated to them. Introduction. The concept of bi-(or multi-)Hamiltonian structures on ...
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