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

Özlem Orhan; Teoman Özer

doi:10.1186/s13662-016-0966-4

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

Özlem Orhan, Teoman Özer^*

^*Corresponding author for this work

Department of Civil Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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˙ + B(t, x) , the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the λ-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.

Original language	English
Article number	259
Journal	Advances in Difference Equations
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13662-016-0966-4
Publication status	Published - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, Orhan and Özer.

Keywords

dynamical systems
first integrals
integrating factors
Lagrangian and Hamiltonian description
Prelle-Singer procedure
Sundman transformation
λ-symmetries

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10.1186/s13662-016-0966-4

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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˙ + B(t, x) , the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the λ-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.",

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AU - Orhan, Özlem

AU - Özer, Teoman

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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˙ + B(t, x) , the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the λ-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.

AB - 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˙ + B(t, x) , the corresponding exact solutions and the integrating factors. In addition, we analyze other types of the first integrals via the λ-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.

KW - dynamical systems

KW - first integrals

KW - integrating factors

KW - Lagrangian and Hamiltonian description

KW - Prelle-Singer procedure

KW - Sundman transformation

KW - λ-symmetries

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DO - 10.1186/s13662-016-0966-4

M3 - Article

AN - SCOPUS:84991396328

SN - 1687-1839

VL - 2016

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 259

ER -

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

Abstract

Bibliographical note

Keywords

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