Separation of Variables for Bi-Hamiltonian Systems |
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Authors: | Falqui Gregorio Pedroni Marco |
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Institution: | (1) SISSA, Via Beirut 2/4, I-34014 Trieste, Italy. e-mail;(2) Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy |
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Abstract: | 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 N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the 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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Keywords: | Hamilton– Jacobi equations separation of variables Nijenhuis structures bi-Hamiltonian manifolds |
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