Open AccessOn Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type
Author(s) -
M. ti,
K. K. D. Adjaï,
J. Akande,
M. D. Monsia
Publication year - 2021
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-19-2021-970
Subject(s) - mathematics , type (biology) , nonlinear system , jacobi elliptic functions , quadratic equation , class (philosophy) , polynomial , differential equation , elliptic function , mathematical analysis , plane (geometry) , phase plane , computer science , physics , geometry , ecology , quantum mechanics , artificial intelligence , biology
In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.