Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems

CHEN Yang-yang; YAN Le-wei; SZE Kam-yim; CHEN Shu-hui

doi:10.3879/j.issn.1000-0887.2012.09.004

Volume 33 Issue 9

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Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(9): 1064-1077

CHEN Yang-yang, YAN Le-wei, SZE Kam-yim, CHEN Shu-hui. Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1064-1077. doi: 10.3879/j.issn.1000-0887.2012.09.004

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Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems

doi: 10.3879/j.issn.1000-0887.2012.09.004

Received Date: 2012-05-08
Rev Recd Date: 2012-05-16
Publish Date: 2012-09-15

Abstract

Abstract

A generalized hyperbolic perturbation method was presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation procedure was improved for those systems whose exact homoclinic generating solutions could not be explicitly derived. The generalized hyperbolic functions were employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic and quartic nonlinearity were studied in details to illustrate the efficiency and accuracy of the present method.
- generalized hyperbolic perturbation method,
- nonlinear autonomous systems,
- homoclinic solution

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References

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