Exact analytic solutions for the damped Duffing nonlinear oscillator
type: Item
instance of: scholarly article
title: Exact analytic solutions for the damped Duffing nonlinear oscillator
zbMATH Open document ID: 1119.34002
author: D. E. Panayotounakos
author: Michalis P. Markakis
author: E. E. Theotokoglou
published in: Comptes Rendus. Mécanique. Académie des Sciences, Paris
publication date: 2007-03-02T00:00:00Z
review text: In two previous papers the authors found a closed form solution for the normal form \[ yy'-y=f(x) \] of the Abel equation of the second kind. In the given paper, the authors reduce the damped Duffing oscillator to such an equation, so that it becomes also possible to solve this equation. A complication arises from the fact that the solutions may change its character at some point which must be determined. Furthermore, the explicit determination of the solution requires to solve transcendental equations which is usually only approximately possible.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 70K99
zbMATH DE Number: 5130320
zbMATH Keywords: Duffing oscillator
zbMATH Keywords: Abel equation
MaRDI profile type: Publication
full work available at URL: j.crme.2006.03.009
OpenAlex ID: W2098324627
DOI: 10.1016/J.CRME.2006.03.009
description: scientific article; zbMATH DE number 5130320