Submitting Campus

Daytona Beach

Department

Department of Mathematics

Document Type

Article

Publication/Presentation Date

1-2016

Abstract/Description

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.

Publication Title

Physics Letters A

DOI

https://doi.org/10.1016/j.physleta.2015.11.009

Publisher

Elsevier

Included in

Mathematics Commons

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