Solutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman Transformation
Authors:
- Damien Kolawolé Kêgnidé AdjaïDADamien Kolawolé Kêgnidé Adjaï
- Yélomè Judicaë Fernando KpomahouYKYélomè Judicaë Fernando Kpomahou
- Marc Delphin MonsiaMMMarc Delphin Monsia
Open Access
- 1 January 2018
- journal article
- Published by Science Publications in Journal of Mathematics and Statistics
- Vol. 14 (1) , 241-252
Abstract
A new approach using the generalized Sundman transformation to solve explicitly and exactly in a straightforward manner the cubic elliptic Duffing equation is proposed in this study. The method has the advantage to closely relate this equation to the linear harmonic oscillator equation and to be applied to solve other nonlinear differential equations. As a result, explicit and exact general periodic solutions to some Painlevé-Gambier type equations have been established and in particular, it is shown that a reduced Painlevé-Gambier XII equation can exhibit trigonometric solutions, but with a shift factor.Keywords
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