Separation of variables for bi-Hamiltonian systems

Details Separation of variables for bi-Hamiltonian systems Separation of variables for bi-Hamiltonian systems

2002-04-15

arxiv.org/abs/nlin/0204029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex, 47 pages

Scientific paper

We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.

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