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2012 Lie and Riccati Linearization of a Class of Liénard Type Equations
A. G. Johnpillai, C. M. Khalique, F. M. Mahomed
J. Appl. Math. 2012(SI14): 1-8 (2012). DOI: 10.1155/2012/171205


We construct a linearizing Riccati transformation by using an ansatz and a linearizing point transformation utilizing the Lie point symmetry generators for a three-parameter class of Liénard type nonlinear second-order ordinary differential equations. Since the class of equations also admits an eight-parameter Lie group of point transformations, we utilize the Lie-Tresse linearization theorem to obtain linearizing point transformations as well. The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equations, respectively. The general solution of this class of equations can then easily be obtained by integrating the linearized equations resulting from both of the linearization approaches. A comparison of the results deduced in this paper is made with the ones obtained by utilizing an approach of mapping the class of equations by a complex point transformation into the free particle equation. Moreover, we utilize the linearizing Riccati transformation to extend the underlying class of equations, and the Lie-Tresse linearization theorem is also used to verify the conditions of linearizability of this new class of equations.


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A. G. Johnpillai. C. M. Khalique. F. M. Mahomed. "Lie and Riccati Linearization of a Class of Liénard Type Equations." J. Appl. Math. 2012 (SI14) 1 - 8, 2012.


Published: 2012
First available in Project Euclid: 16 July 2013

zbMATH: 1270.34079
MathSciNet: MR3000291
Digital Object Identifier: 10.1155/2012/171205

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI14 • 2012
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