IJPAM: Volume 82, No. 3 (2013)

AROUND COMPLETE CLASSIFICATION OF
LIÉNARD EQUATION AND APPLICATION

Halim Zeghdoudi$^{1,3}$, Raouf Dridi$^2$,
Mohamed Riad Remita$^3$, Lahsen Bouchahed$^{3}$
$^1$Department Computing Mathematics and Physics
Waterford Institute of Technology
Waterford, IRELAND
$^2$Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z1, CANADA
$^3$LaPS laboratory
Badji-Mokhtar University
Box 12, Annaba, 23000, ALGERIA


Abstract. In this paper, we present a complete symmetry classification of Liénard equation ${\ddot{x}=f(x)\dot{x}+g(x)}$. The transformations we consider are of the form ${(t,x)\rightarrow (at+\alpha (x),\ \beta (x))}$. They preserve the set of periodic solutions. The machinery used to accomplish this complete classification is Ritt-Kolchin's theory of characteristic sets. Also, we give an example presented in work of J. Goard $\left[ 7\right] $, who using Lie symmetry methods in finance.

Received: October 24, 2012

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 3