Mathematics – Functional Analysis
Scientific paper
Oct 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1283..268b&link_type=abstract
MATHEMATICS AND ASTRONOMY: A JOINT LONG JOURNEY: Proceedings of the International Conference. AIP Conference Proceedings, Volum
Mathematics
Functional Analysis
Oscillators, Lie Algebras, Integral Equations, Functional Analysis, Oscillators, Pulse Generators, And Function Generators, Lie Algebras Of Lie Groups, Integral Equations, Functional Analysis
Scientific paper
A constructive method to obtain integrable Hamiltonians with N degrees of freedom is presented. This approach is based on the h6 Poisson coalgebra and allows us to construct two new families of nonlinear integrable perturbations of the N-dimensional oscillator. The first one is a family of integrable perturbations depending on N parameters and two arbitrary functions, and it includes as particular cases several known quartic and sextic coupled nonlinear oscillators. The second type of integrable perturbations contains homogeneous functions with degree -2 in the coordinates together with an arbitrary radial function. In all the cases, the integrals of the motion are explicitly given.
Ballesteros Angel
Blasco Alfonso
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