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Two important examples of nonlinear oscillators

José F. Cariñena·Manuel F. Rañada·Mariano Santander
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Abstract

We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This oscillator can be seen as a position-dependent mass system and we show a natural quantization prescription admitting a factorization with shape invariance for the $n=1$ case, and then the energy spectrum is found. Other isochronous systems which can also be considered as a generalization of the harmonic oscillator and admit a nonstandard Lagrangian description are also discussed.

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José F. Cariñena, Manuel F. Rañada, Mariano Santander. 2005-05-10. Two important examples of nonlinear oscillators. https://arxiv.org/abs/math-ph/0505028

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