Asymptotic expansions of the period solutions of nonlinear evolution equations
type: Item
instance of: scholarly article
title: Asymptotic expansions of the period solutions of nonlinear evolution equations
zbMATH Open document ID: 0905.34031
DOI: 10.1023/A:1008203813615
author: S. H. Smith
published in: Nonlinear Dynamics
publication date: 1998-08-09T00:00:00Z
review text: A spectral technique for building asymptotic expansions which describe periodic processes in conservative and self-excited systems is presented. The small parameter of the expansion is connected with the ratio of the amplitudes of higher than the first harmonics. In the case of an oscillator with power nonlinearity the frequency of the main harmonic and the complex amplitudes of higher harmonics are computed. In the simplest case of weakly nonlinear oscillations the complete asymptotic expansion is shown to be valid in the whole domain of the periodic motions of definite type until the separatrix is reached. For some special cases of strongly nonlinear oscillations the comparison of the results with known exact solutions is carried out and criteria of convergence of the expansions are determined.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 1185503
zbMATH Keywords: periodic solutions
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: oscillator
zbMATH Keywords: nonlinearity
zbMATH Keywords: weakly nonlinear oscillations
zbMATH Keywords: separatrix
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: a:1008203813615
OpenAlex ID: W154431037
description: scientific article; zbMATH DE number 1185503