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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Theory of Exact Trigonometric Periodic Solutions to Quadratic Liénard Type Equations

Jean Akande1, Damien Kolawolé Kêgnidé Adjaï 1 and Marc Delphin Monsia1
  • 1 University of Abomey-Calavi, Benin

Abstract

A 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 elliptic functions is highlighted by some illustrative examples.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 232-240

DOI: https://doi.org/10.3844/jmssp.2018.232.240

Submitted On: 12 June 2018 Published On: 29 October 2018

How to Cite: Akande, J., Kêgnidé Adjaï , D. K. & Monsia, M. D. (2018). Theory of Exact Trigonometric Periodic Solutions to Quadratic Liénard Type Equations. Journal of Mathematics and Statistics, 14(1), 232-240. https://doi.org/10.3844/jmssp.2018.232.240

Open AccessCopyright: © 2018 Jean Akande, Damien Kolawolé Kêgnidé Adjaï and Marc Delphin Monsia. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Liénard Equations
  • Painlevé-Gambier Equations
  • Periodic Solution
  • Generalized Sundman Transformation