Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation
American Journal of Physics and Applications
Volume 3, Issue 5, September 2015, Pages: 159-165
Received: Jul. 8, 2015; Accepted: Jul. 16, 2015; Published: Jul. 25, 2015
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Authors
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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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.
Keywords
Cubic-Quintic Duffing Equation, Heteroclinic and the Homoclinic Solutions, Soliton
To cite this article
Serge Bruno Yamgoué, Jules Hilaire Kamga, Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation, American Journal of Physics and Applications. Vol. 3, No. 5, 2015, pp. 159-165. doi: 10.11648/j.ajpa.20150305.11
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