Lie and Riccati Linearization of a Class of Liénard Type Equations
Joint Authors
Khalique, Chaudry Masood
Johnpillai, Andrew Gratien
Mahomed, Fazal Mahmood
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-09
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Johnpillai, Andrew Gratien& Khalique, Chaudry Masood& Mahomed, Fazal Mahmood. 2012. Lie and Riccati Linearization of a Class of Liénard Type Equations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-993002
Modern Language Association (MLA)
Johnpillai, Andrew Gratien…[et al.]. Lie and Riccati Linearization of a Class of Liénard Type Equations. Journal of Applied Mathematics No. 2012 (2012), pp.1-8.
https://search.emarefa.net/detail/BIM-993002
American Medical Association (AMA)
Johnpillai, Andrew Gratien& Khalique, Chaudry Masood& Mahomed, Fazal Mahmood. Lie and Riccati Linearization of a Class of Liénard Type Equations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-8.
https://search.emarefa.net/detail/BIM-993002
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993002