Generalized nonlinear oscillators with quasi-harmonic behaviour: classical solutions

TL;DR

This paper generalizes the classical nonlinear oscillator by adding potential terms, revealing more complex solution behaviors than the original model, thus expanding understanding of quasi-harmonic systems.

Contribution

It introduces two new generalizations of the nonlinear oscillator with additional potential terms, demonstrating richer dynamical behaviors.

Findings

Solutions exhibit more complex patterns than original oscillator

Generalizations include additional potential terms

Richer behavior patterns are analytically shown

Abstract

The classical nonlinear oscillator, proposed by Mathews and Lakshmanan in 1974 and including a position-dependent mass in the kinetic energy term, is generalized in two different ways by adding an extra term to the potential. The solutions of the Euler-Lagrange equation are shown to exhibit richer behaviour patterns than those of the original nonlinear oscillator.