Article
Existence of Periodic Orbits in Nonlinear Oscillators of Emden-Fowler Form
Physics Letters A
(2016)
Abstract
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context.
Disciplines
Publication Date
January 28, 2016
DOI
https://doi.org/10.1016/j.physleta.2015.11.009
Citation Information
S.C. Mancas and Haret C. Rosu. "Existence of Periodic Orbits in Nonlinear Oscillators of Emden-Fowler Form" Physics Letters A Vol. 380 Iss. 3 (2016) p. 422 - 428 Available at: http://works.bepress.com/stefani_mancas/100/