Trihamiltonian extensions of separable systems in the plane

Details Trihamiltonian extensions of separable systems in the plane Trihamiltonian extensions of separable systems in the plane

2004-07-13

arxiv.org/abs/nlin/0407030v1

J. Math. Phys. 47, 043505 (2006) (22 pages)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages

Scientific paper

10.1063/1.2188227

A method to construct trihamiltonian extensions of a separable system is presented. The procedure is tested for systems, with a natural Hamiltonian, separable in classical sense in one of the four orthogonal separable coordinate systems of the Euclidean plane, and some explicit examples are constructed. Finally a conjecture on possible generalizations to other classes of systems is discussed: in particular, the method can be easily adapted to the eleven orthogonal separable coordinate sets of the Euclidean three-space.

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