Transition from pulses to fronts in the cubic-quintic complex Ginzburg-Landau equation

Pablo Gutiérrez; Daniel Escaff; Orazio Descalzi

doi:10.1098/rsta.2009.0073

Transition from pulses to fronts in the cubic-quintic complex Ginzburg-Landau equation

Pablo Gutiérrez^*, Daniel Escaff, Orazio Descalzi

^*Corresponding author for this work

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

6 Scopus citations

Abstract

The cubic-quintic complex Ginzburg-Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov-Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts.This fact is consistent with numerical simulations.

Original language	English
Pages (from-to)	3227-3238
Number of pages	12
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	367
Issue number	1901
DOIs	https://doi.org/10.1098/rsta.2009.0073
State	Published - 28 Aug 2009

Keywords

Bifurcations
Ginzburg-Landau equation
Localized structures

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10.1098/rsta.2009.0073

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abstract = "The cubic-quintic complex Ginzburg-Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov-Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts.This fact is consistent with numerical simulations.",

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author = "Pablo Guti{\'e}rrez and Daniel Escaff and Orazio Descalzi",

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AU - Gutiérrez, Pablo

AU - Escaff, Daniel

AU - Descalzi, Orazio

PY - 2009/8/28

Y1 - 2009/8/28

N2 - The cubic-quintic complex Ginzburg-Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov-Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts.This fact is consistent with numerical simulations.

AB - The cubic-quintic complex Ginzburg-Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov-Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts.This fact is consistent with numerical simulations.

KW - Bifurcations

KW - Ginzburg-Landau equation

KW - Localized structures

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JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1901

ER -

Transition from pulses to fronts in the cubic-quintic complex Ginzburg-Landau equation

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Keywords

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