TY - JOUR
A2 - Qadir, Asghar
AU - Johnpillai, A. G.
AU - Khalique, C. M.
AU - Mahomed, F. M.
PY - 2012
DA - 2012/12/09
TI - Lie and Riccati Linearization of a Class of LiĆ©nard Type Equations
SP - 171205
VL - 2012
AB - 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.
SN - 1110-757X
UR - https://doi.org/10.1155/2012/171205
DO - 10.1155/2012/171205
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -