Analysis of Lienard II-type oscillator equation by symmetry-transformation methods


Orhan O. , Özer T.

ADVANCES IN DIFFERENCE EQUATIONS, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2016
  • Doi Number: 10.1186/s13662-016-0966-4
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS

Abstract

In this study, we consider a Lienard II-type harmonic nonlinear oscillator equation as a nonlinear dynamical system. Firstly, we examine the first integrals in the form A(t, x)(x)over dot + B( t, x), the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the lambda-symmetry approach. We show that the equation can be linearized by means of a nonlocal transformation, the so-called Sundman transformation. Furthermore, using the modified Prelle-Singer approach, we point out that explicit time-independent first integrals can be identified for the Lienard II-type harmonic nonlinear oscillator equation.