On the reduction of nonlinear oscillator-equations to Abel forms
type: Item
instance of: scholarly article
title: On the reduction of nonlinear oscillator-equations to Abel forms
zbMATH Open document ID: 1070.34009
author: Yanyan Li
published in: Applied Mathematics and Computation
publication date: 2004-10-14T00:00:00Z
review text: The author considers the existence of analytical solutions for the nonlinear ordinary differential equations governing the Duffing, Rayleigh and Van der Pol oscillators. These equations represent a subset of a larger class of particular ordinary differential equations in mathematical physics, governing problems with strong nonlinearities. There are made several efforts to obtain solutions for the nonlinear ordinary differential equations considered in this paper. However, exact analytical solutions in terms of known functions are still lacking. Here, the author using a series of functional transformations, finally reduces all equations considered in the paper to Abel's equations of second kind that do not have exact analytical solutions.
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 2107894
zbMATH Keywords: nonlinear oscillators
zbMATH Keywords: reduction to Abel's equations
zbMATH Keywords: Duffing and Van der Pol equations
zbMATH Keywords: nonlinear ordinary differential equations
reviewed by: S. D. Bajpai
MaRDI profile type: Publication
full work available at URL: j.amc.2003.08.038
OpenAlex ID: W2018848804
cites work: Q3292729
cites work: The generalized Duffing equation with large damping
cites work: Transitions from strongly to weakly nonlinear motions of damped nonlinear oscillators
cites work: On the solution of the unforced damped Duffing oscillator with no linear stiffness term
cites work: Q5735351
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q4067388
cites work: On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k Large
cites work: Q4890882
cites work: Q5567096
DOI: 10.1016/J.AMC.2003.08.038
description: scientific article; zbMATH DE number 2107894