In this paper we try to outline, in a simple and informal way, some of the deep links connecting the classical theory of separation of variables (of the Hamilton-Jacobi equations) and the geometry of bihamiltonian manifold. Our aim is to present a new "test of separability" for a special class of Hamiltonian integrable systems defined on bihamiltonian manifolds. This class contains the Gel'fand-Zakharevich systems, which play an important role in the theory of soliton equations. This paper is a kind of introduction to a forthcoming paper of the same authors, to which we refer for more details, proofs, and references
Falqui, G., Magri, F., Pedroni, M. (2000). A bihamiltonian approach to separation of variables in mechanics. In M. Boiti, L. Martina, F. Pempinelli, B. Prinari, G. Soliani (a cura di), PROCEEDINGS OF THE WORKSHOP ON NONLINEARITY, INTEGRABILITY AND ALL THAT: TWENTY YEARS AFTER NEEDS '79 (pp. 258-266). WORLD SCIENTIFIC PUBL CO PTE LTD.
A bihamiltonian approach to separation of variables in mechanics
Falqui, G;Magri, F;
2000
Abstract
In this paper we try to outline, in a simple and informal way, some of the deep links connecting the classical theory of separation of variables (of the Hamilton-Jacobi equations) and the geometry of bihamiltonian manifold. Our aim is to present a new "test of separability" for a special class of Hamiltonian integrable systems defined on bihamiltonian manifolds. This class contains the Gel'fand-Zakharevich systems, which play an important role in the theory of soliton equations. This paper is a kind of introduction to a forthcoming paper of the same authors, to which we refer for more details, proofs, and references
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