Detection of standing pulses in periodic media by pulse interaction
type: Item
instance of: scholarly article
title: Detection of standing pulses in periodic media by pulse interaction
zbMATH Open document ID: 1259.78030
author: Martina Chirilus-Bruckner
author: Guido Schneider
published in: Journal of Differential Equations
publication date: 2012-08-24T00:00:00Z
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 6071619
zbMATH Keywords: Klein-Gordon equation
MaRDI profile type: Publication
full work available at URL: j.jde.2012.06.003
OpenAlex ID: W1995586265
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DOI: 10.1016/J.JDE.2012.06.003
review text: The paper addresses the nonlinear Klein-Gordon equation with spatially periodic coefficients \(a(x)\) and \(b(x)\) NEWLINE\[NEWLINE u_{tt} = u_{xx} -a(x)u + b(x)u^3. NEWLINE\]NEWLINE The objective is to study, by means of analytical methods, the dynamics of approximate soliton solutions in this model, especially collisions between quiescent and moving solitons. The analysis uses the Fourier transform of the field, then returning to the \(x\)-space. The main problem is the separation of the internal and external dynamics of the colliding solitons. It is suggested that the elaborated method may find applications to more general models of nonlinear disperive media with spatially periodic coefficients.
description: scientific article; zbMATH DE number 6071619