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 omegaN manifolds, to give intrisic tests of separability ( and Stackel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omegaN 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

Falqui, G., Pedroni, M. (2003). Separation of variables for bi-Hamiltonian systems. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 6(2), 139-179 [10.1023/A:1024080315471].

Separation of variables for bi-Hamiltonian systems

Falqui, G;Pedroni, M
2003

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 omegaN manifolds, to give intrisic tests of separability ( and Stackel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omegaN 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
Articolo in rivista - Articolo scientifico
Hamilton-Jacobi equations; separation of variables; Nijenhuis structures; bi-Hamiltonian manifolds
English
2003
6
2
139
179
none
Falqui, G., Pedroni, M. (2003). Separation of variables for bi-Hamiltonian systems. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 6(2), 139-179 [10.1023/A:1024080315471].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/20270
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