3 results for “Liénard Equation”

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Research ArticleOpen accessEvery word in the titleTheory 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 accessEvery word in the titleExact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard TypeLucas H. Koudahoun, Jean Akande, Damien K.K. Adjaï et al.Authors introduce a generalized singular differential equation of quadratic Liénard type for study of exact classical and quantum mechanical solutions. The equation is shown to exhibit periodic solutions and to include the linear harmonic oscillator equation and the Painlevé-Gambier XVII equation as special cases. It is also shown that the equation may exhibit discrete eigenstates as quantum behavior under Nikiforov-Uvarov … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 5 Jul 2018 · 7,609 accessesView PDF Cite

Research ArticleOpen accessIn the abstractOn 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