Monotonous property of non-oscillations of the damped Duffing's equation
type: Item
instance of: scholarly article
title: Monotonous property of non-oscillations of the damped Duffing's equation
zbMATH Open document ID: 1097.34026
published in: Chaos, Solitons and Fractals
publication date: 2006-02-13T00:00:00Z
review text: This paper deals with the monotony property of the bounded nonoscillations for the damped Duffing equation \[ \ddot x+\delta\dot x-\mu x+ x^3= 0, \] where \(\delta\) is the damping coefficient. The author is interested in establishing analytic results. It is shown that under suitable assumptions on \(\delta\) and \(\mu\), the only two nontrivial bounded exact solutions are monotone: one is monotone decreasing and the other one is monotone increasing. An explicit exact solution is obtained by a direct method. This approach is used to obtain travelling waves solutions of reaction-diffusion equations.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 5005529
zbMATH Keywords: Duffing's equation
zbMATH Keywords: nonoscillations
zbMATH Keywords: monotony property
zbMATH Keywords: autonomous system
zbMATH Keywords: exact solutions
author: Zhaosheng Feng
MaRDI profile type: Publication
full work available at URL: j.chaos.2005.07.006
OpenAlex ID: W2045028208
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DOI: 10.1016/J.CHAOS.2005.07.006
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description: scientific article; zbMATH DE number 5005529