Analytical solution of the damped Helmholtz-Duffing equation
type: Item
instance of: scholarly article
title: Analytical solution of the damped Helmholtz-Duffing equation
zbMATH Open document ID: 1259.34004
author: Alex Elías-Zúñiga
published in: Applied Mathematics Letters
publication date: 2012-10-11T00:00:00Z
review text: Consider the differential equation \[ \ddot x+ Ax+ 2\nu\dot x+ Bx^2+\varepsilon x^3= 0.\tag{\(*\)} \] Under the assumption \(A= {3B^2+ 8\varepsilon\nu\over 9\varepsilon}\), the author derives an analytic solution of equation \((*)\) by using Jacobian elliptic functions.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6092822
zbMATH Keywords: mixed-parity nonlinear oscillator
zbMATH Keywords: quadratic nonlinearities
zbMATH Keywords: damped Helmholtz-Duffing oscillator
zbMATH Keywords: asymmetric behavior
MaRDI profile type: Publication
full work available at URL: j.aml.2012.06.030
OpenAlex ID: W1981030281
cites work: Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method—I: The fundamental mode of isotropic plates
cites work: Exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator
cites work: Monotonous property of non-oscillations of the damped Duffing's equation
cites work: New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems
cites work: Integrability and symmetries for the Helmholtz oscillator with friction
DOI: 10.1016/J.AML.2012.06.030
description: scientific article; zbMATH DE number 6092822