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
Citation: 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

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
  • 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.
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