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A geometric approach to the separability of the Neumann-Rosochatius system. (English) Zbl 1051.37036

Summary: 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.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
53D17 Poisson manifolds; Poisson groupoids and algebroids
70H20 Hamilton-Jacobi equations in mechanics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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