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A geometric approach to the separability of the Neumann-Rosochatius system

Claudio Bartocci·Gregorio Falqui·Marco Pedroni
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Abstract

We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.

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Claudio Bartocci, Gregorio Falqui, Marco Pedroni. 2003-07-12. A geometric approach to the separability of the Neumann-Rosochatius system. https://arxiv.org/abs/nlin/0307021

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