Integrable perturbations of the N-dimensional isotropic oscillator

Details Integrable perturbations of the N-dimensional isotropic oscillator Integrable perturbations of the N-dimensional isotropic oscillator

2009-08-07

arxiv.org/abs/0908.1017v2

Physics Letters A 374 (2010) 2218-2224

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, revised version, content changed and new references

Scientific paper

10.1016/j.physleta.2010.03.040

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h_6-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N-1) `Rosochatius' terms that preserve the complete integrability of all these models.

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