3 results for “Generalized Sundman Transformation”

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Research ArticleOpen accessPhrase in the titleSolutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman TransformationDamien Kolawolé Kêgnidé Adjaï, Lucas Hervé Koudahoun, Jean Akande et al.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 … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 8 Nov 2018 · 7,251 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsTheory of Exact Trigonometric Periodic Solutions to Quadratic Liénard Type EquationsJean Akande, Damien Kolawolé Kêgnidé Adjaï, Marc Delphin MonsiaA mathematical theory is developed through generalized Sundman transformation to show the existence of classes of quadratic Liénard type equations which admit exact and explicit general trigonometric solutions but with amplitude-dependent frequency. The application of the theory to compute also exact and explicit general periodic solutions to nonlinear differential equations like inverted Painlevé-Gambier equations in terms of trigonometric or Jacobian … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 29 Oct 2018 · 7,215 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsOn the General Solution to the Bratu and Generalized Bratu EquationsLucas Hervé Koudahoun, Jean Akande, Damien Kêgnidé Kolawolé Adjaï et al.This work shows that the Bratu equation belongs to a general class of Liénard-type equations for which the general solution may be exactly and explicitly computed within the framework of the generalized Sundman transformation. In this perspective the exact solution of the Bratu nonlinear two-point boundary value problem as well as of some well-known Bratu-type problems have been determined. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 14 Jul 2018 · 7,686 accessesView PDF Cite