Two important examples of nonlinear oscillators

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.

References in corpus (3)

• A systematic study on the exact solution of the position dependent mass Schroedinger equation
• One-dimensional model of a quantum nonlinear harmonic oscillator
• Riccati equation, Factorization Method and Shape Invariance

Cited by in corpus (7)

• A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
• Nonlinear Dynamics of a position-dependent mass driven Duffing-type oscillator
• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations
• Classical oscillator with position-dependent mass in a complex domain
• Superintegrable classical Zernike system
• Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
• Qualitative analysis of certain generalized classes of quadratic oscillator systems