American Journal of Physics and Applications

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Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation

Received: 08 July 2015    Accepted: 16 July 2015    Published: 25 July 2015
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Abstract

In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which also represent solitons of some wave equations are carefully analyzed.

DOI 10.11648/j.ajpa.20150305.11
Published in American Journal of Physics and Applications (Volume 3, Issue 5, September 2015)
Page(s) 159-165
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Cubic-Quintic Duffing Equation, Heteroclinic and the Homoclinic Solutions, Soliton

References
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[14] N. Srinil, and H. Zanganeh, ‘‘Modelling of coupled cross-flow/in-line vortex-induced vibrations using double Duffing and van der Pol oscillators’’, Ocean Engineering, Vol. 53, pp. 83–97, 2012.
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Author Information
  • Department of Physics, Higher Teacher Training College-Bambili, The University of Bamenda, Bamenda, Cameroon

  • Laboratoire de Mécanique et de Modélisation des Systèmes Physiques (L2MSP), Département de Physique, Université de Dschang, Dschang, Cameroun

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    Serge Bruno Yamgoué, Jules Hilaire Kamga. (2015). Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation. American Journal of Physics and Applications, 3(5), 159-165. https://doi.org/10.11648/j.ajpa.20150305.11

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    ACS Style

    Serge Bruno Yamgoué; Jules Hilaire Kamga. Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation. Am. J. Phys. Appl. 2015, 3(5), 159-165. doi: 10.11648/j.ajpa.20150305.11

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    AMA Style

    Serge Bruno Yamgoué, Jules Hilaire Kamga. Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation. Am J Phys Appl. 2015;3(5):159-165. doi: 10.11648/j.ajpa.20150305.11

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  • @article{10.11648/j.ajpa.20150305.11,
      author = {Serge Bruno Yamgoué and Jules Hilaire Kamga},
      title = {Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation},
      journal = {American Journal of Physics and Applications},
      volume = {3},
      number = {5},
      pages = {159-165},
      doi = {10.11648/j.ajpa.20150305.11},
      url = {https://doi.org/10.11648/j.ajpa.20150305.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpa.20150305.11},
      abstract = {In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which also represent solitons of some wave equations are carefully analyzed.},
     year = {2015}
    }
    

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    AB  - In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which also represent solitons of some wave equations are carefully analyzed.
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