Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation

Serge Bruno Yamgoué; Jules Hilaire Kamga

doi:doi:10.11648/j.ajpa.20150305.11

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Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation

Serge Bruno Yamgoué, Jules Hilaire Kamga

Published in American Journal of Physics and Applications (Volume 3, Issue 5)

Received: 8 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.

Published in	American Journal of Physics and Applications (Volume 3, Issue 5)
DOI	10.11648/j.ajpa.20150305.11
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), 2015. Published by Science Publishing Group

Keywords

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

References

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation
AU  - Serge Bruno Yamgoué
AU  - Jules Hilaire Kamga
Y1  - 2015/07/25
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150305.11
DO  - 10.11648/j.ajpa.20150305.11
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 159
EP  - 165
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150305.11
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.
VL  - 3
IS  - 5
ER  -

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Author Information

Serge Bruno Yamgoué

Department of Physics, Higher Teacher Training College-Bambili, The University of Bamenda, Bamenda, Cameroon
Jules Hilaire Kamga

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

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APA Style

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation
AU  - Serge Bruno Yamgoué
AU  - Jules Hilaire Kamga
Y1  - 2015/07/25
PY  - 2015
N1  - https://doi.org/10.11648/j.ajpa.20150305.11
DO  - 10.11648/j.ajpa.20150305.11
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 159
EP  - 165
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20150305.11
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.
VL  - 3
IS  - 5
ER  -

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