Coherence and chaos in the driven damped sine-Gordon equation: measurement of the soliton spectrum
type: Item
instance of: scholarly article
title: Coherence and chaos in the driven damped sine-Gordon equation: measurement of the soliton spectrum
zbMATH Open document ID: 0615.35071
DOI: 10.1016/0167-2789(86)90052-7
author: A. R. Bishop
author: Edward A. II Overman
author: David W. McLaughlin
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field \((\phi,\phi_ t)\) which is periodic in space. The procedure is applied to the field generated by a damped, driven sine-Gordon equation. This field can be either temporally periodic (locked to the driver) or chaotic. In either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized (soliton wave-train) modes. The numerical procedure quantitatively identifies the presence, number and properties of these soliton wave-trains. For example, an increase of spatial symmetry is accompanied by the injection of additional solitons into the field.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 65N99
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 3996263
zbMATH Keywords: numerical procedure
zbMATH Keywords: sine-Gordon soliton
zbMATH Keywords: radiation content
zbMATH Keywords: periodic in space
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: temporally periodic
zbMATH Keywords: chaotic
zbMATH Keywords: soliton wave- train
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90052-7
OpenAlex ID: W2047686001
cites work: Influence of solitons in the initial state on chaos in the driven damped sine-Gordon system
cites work: Q3718109
cites work: Nonlinear normal modes for the Toda chain
cites work: Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint
cites work: The origin and saturation of modulational instabilities
cites work: Q5180217
description: scientific article; zbMATH DE number 3996263