A non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators

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dc.creatorCariñena, José F.
dc.creatorRañada, Manuel F.
dc.creatorSantander, Mariano
dc.creatorSenthilvelan, Murugaian
dc.date2004-06-01
dc.date.accessioned2026-07-07T11:10:37Z
dc.date.available2026-07-07T11:10:37Z
dc.descriptionA nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at the quantum level. First, it is proved that it is a super-integrable system, and then the nonlinear equations are solved and the solutions are explicitly obtained. All the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. In the second part the system is generalized to the case of $n$ degrees of freedom. Finally, the relation of this nonlinear system with the harmonic oscillator on spaces of constant curvature, two-dimensional sphere $S^2$ and hyperbolic plane $H^2$, is discussed.
dc.description30 pages, 4 figures, submitted to Nonlinearity
dc.identifierhttps://arxiv.org/abs/math-ph/0406002
dc.identifierhttp://arxiv.org/abs/math-ph/0406002
dc.identifierNonlinearity17:1941-1963,2004
dc.identifierdoi:10.1088/0951-7715/17/5/019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190831
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.subject37J35, 34A34, 34C15, 70H06
dc.titleA non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators
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