Coherence and chaos in the driven damped sine-gordon equation: Measurement of the soliton spectrum

E. A. Overman, D. W. McLaughlin, A. R. Bishop

Research output: Contribution to journalArticle

Abstract

A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (φ, φt) 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.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalPhysica D: Nonlinear Phenomena
Volume19
Issue number1
DOIs
StatePublished - 1986

Fingerprint

sine-Gordon equation
Sine-Gordon Equation
Solitons
Chaos theory
Damped
chaos
Chaos
solitary waves
Numerical Procedure
Spatial Structure
Driver
Injection
Radiation
injection
Symmetry
symmetry
radiation

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Coherence and chaos in the driven damped sine-gordon equation : Measurement of the soliton spectrum. / Overman, E. A.; McLaughlin, D. W.; Bishop, A. R.

In: Physica D: Nonlinear Phenomena, Vol. 19, No. 1, 1986, p. 1-41.

Research output: Contribution to journalArticle

@article{74846bd1edbf41a5aad1734f2fe8f87b,
title = "Coherence and chaos in the driven damped sine-gordon equation: Measurement of the soliton spectrum",
abstract = "A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (φ, φt) 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.",
author = "Overman, {E. A.} and McLaughlin, {D. W.} and Bishop, {A. R.}",
year = "1986",
doi = "10.1016/0167-2789(86)90052-7",
language = "English (US)",
volume = "19",
pages = "1--41",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Coherence and chaos in the driven damped sine-gordon equation

T2 - Measurement of the soliton spectrum

AU - Overman, E. A.

AU - McLaughlin, D. W.

AU - Bishop, A. R.

PY - 1986

Y1 - 1986

N2 - A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (φ, φt) 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.

AB - A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (φ, φt) 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.

UR - http://www.scopus.com/inward/record.url?scp=0010499171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010499171&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(86)90052-7

DO - 10.1016/0167-2789(86)90052-7

M3 - Article

VL - 19

SP - 1

EP - 41

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1

ER -