A complete Classification of Lienard equation

Authors

  • Halim Zeghdoudi LANOS laboratory, Badji-Mokhtar University, BP12, Annaba 23000-Algeria
  • Lahsen Bouchahed
  • Raouf Dridi Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z1, Canada

Keywords:

Li´enard equation, Lie’s symmetries, Characteristic sets

Abstract

We consider scalar Liénard equations

¨x(t) = f (x(t))˙x(t)+ g(x(t)), x(t) 2R(1)

and the diffeomorphisms ' : R2!R2 in the form

phi(x, t) = (beta(x), a.t +apha(x))(2)

where the derivative of the function is non zero and where the real number a is non zero. The aim

result of this paper is to study the symmetries in the form given by (2) for the equation (1).

Author Biographies

  • Halim Zeghdoudi, LANOS laboratory, Badji-Mokhtar University, BP12, Annaba 23000-Algeria
    Mathematical departement, Badji-Mokhtar University, BP12, Annaba 23000-Algeria
  • Raouf Dridi, Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
    University of British Columbia, Vancouver, BC V6T 1Z1, Canada

Downloads

Published

2013-05-01

Issue

Vol. 6 No. 2: (April 2013)

Section

Differential Equations

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

A complete Classification of Lienard equation. (2013). European Journal of Pure and Applied Mathematics, 6(2), 126-136. https://www.ejpam.com/index.php/ejpam/article/view/1099