# A Group Theoretical Identification of Integrable Equations in the Liénard Type Equation $ddot{x} fxdot{x} gx = 0$ : Part II: Equations having Maximal Lie Point Symmetries - Nonlinear Sciences > Exactly Solvable and Integrable

A Group Theoretical Identification of Integrable Equations in the Liénard Type Equation $ddot{x} fxdot{x} gx = 0$ : Part II: Equations having Maximal Lie Point Symmetries - Nonlinear Sciences > Exactly Solvable and Integrable - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this second of the set of two papers on Lie symmetry analysis of a classof Li\-enard type equation of the form $\ddot {x} + fx\dot {x} + gx= 0$,where over dot denotes differentiation with respect to time and $fx$ and$gx$ are smooth functions of their variables, we isolate the equations whichpossess maximal Lie point symmetries. It is well known that any second ordernonlinear ordinary differential equation which admits eight parameter Lie pointsymmetries is linearizable to free particle equation through pointtransformation. As a consequence all the identified equations turn out to belinearizable. We also show that one can get maximal Lie point symmetries forthe above Li\-enard equation only when $f {xx} =0$ subscript denotesdifferentiation. In addition, we discuss the linearising transformations andsolutions for all the nonlinear equations identified in this paper.

Author: ** S. N. Pandey, P. S. Bindu, M. Senthilvelan, M. Lakshmanan**

Source: https://arxiv.org/