Next Article in Journal
On the Redefinition of the Variational and `Partial' Variational Conservation Laws in a Class of Nonlinear PDEs with Mixed Derivatives
Previous Article in Journal
Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow
Article Menu

Article Versions

Export Article

Open AccessArticle
Math. Comput. Appl. 2010, 15(4), 720-731; doi:10.3390/mca15040720

Approximate First Integrals for a System of Two Coupled Van Der Pol Oscillators with Linear Diffusive Coupling

1,* and 2,*
1
Department of Mathematics, School of Science and Engineering, LUMS, Lahore Cantt 54792, Pakistan
2
School of Computational and Applied Mathematics, Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, South Africa
*
Authors to whom correspondence should be addressed.
Published: 1 December 2010
Download PDF [217 KB, uploaded 8 April 2016]

Abstract

The approximate partial Noether operators for a system of two coupled van der Pol oscillators with linear diffusive coupling are presented via a partial Lagrangian approach. The underlying system of two equations, in general, do not admit a standard Lagrangian. However, the approximate first integrals are constructed by utilization of the partial Noether’s theorem with the help of approximate partial Noether operators associated with a partial Lagrangian. These approximate partial Noether operators are not approximate symmetries of the system under study and they do not form an approximate Lie algebra. Moreover, we show how approximate first integrals can be constructed for perturbed ordinary differential equations (ODEs) without making use of a standard Lagrangian.
Keywords: Partial Noether operators; partial Lagrangians; first integrals; van der Pol Partial Noether operators; partial Lagrangians; first integrals; van der Pol
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Naeem, I.; Mahomed, F.M. Approximate First Integrals for a System of Two Coupled Van Der Pol Oscillators with Linear Diffusive Coupling. Math. Comput. Appl. 2010, 15, 720-731.

Show more citation formats Show less citations formats

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top