Traveling hole solutions of the complex Ginzburg-Landau equation: A review

Joceline Lega

doi:10.1016/S0167-2789(01)00174-9

Traveling hole solutions of the complex Ginzburg-Landau equation: A review

Joceline Lega

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

This paper reviews recent works on localized solutions of the one-dimensional complex Ginzburg-Landau (CGL) equation known as traveling holes. Such coherent structures seem to play an important role in the disordered dynamics displayed by CGL at a finite distance past the Benjamin-Feir instability threshold. We discuss these objects in the broader context of weak turbulence and summarize some of their properties.

Original language	English (US)
Pages (from-to)	269-287
Number of pages	19
Journal	Physica D: Nonlinear Phenomena
Volume	152-153
DOIs	https://doi.org/10.1016/S0167-2789(01)00174-9
State	Published - May 15 2001

Keywords

Complex Ginzburg-Landau equation
Phase instability
Traveling hole solutions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(01)00174-9

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title = "Traveling hole solutions of the complex Ginzburg-Landau equation: A review",

abstract = "This paper reviews recent works on localized solutions of the one-dimensional complex Ginzburg-Landau (CGL) equation known as traveling holes. Such coherent structures seem to play an important role in the disordered dynamics displayed by CGL at a finite distance past the Benjamin-Feir instability threshold. We discuss these objects in the broader context of weak turbulence and summarize some of their properties.",

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AB - This paper reviews recent works on localized solutions of the one-dimensional complex Ginzburg-Landau (CGL) equation known as traveling holes. Such coherent structures seem to play an important role in the disordered dynamics displayed by CGL at a finite distance past the Benjamin-Feir instability threshold. We discuss these objects in the broader context of weak turbulence and summarize some of their properties.

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KW - Phase instability

KW - Traveling hole solutions

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ER -

Traveling hole solutions of the complex Ginzburg-Landau equation: A review

Abstract

Keywords

ASJC Scopus subject areas

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