Bihamiltonian geometry and separation of variables for Toda lattices

Abstract

We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifolds, we show that these systems can be explicitly integrated via the classical Hamilton-Jacobi method in the so-called Darboux-Nijenhuis coordinates.

12 pages, Latex with amsmath and amssymb. Report of talks given at NEEDS99

References in corpus (3)

• Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
• Separation of variables for the Dn type periodic Toda lattice
• A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability

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• On the two different bi-Hamiltonian structures for the Toda lattice
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