Sources and sinks in the vicinity of a weakly inverted instability

Jaime Cisternas; Orazio Descalzi

doi:10.1142/S0218127407018804

Sources and sinks in the vicinity of a weakly inverted instability

Jaime Cisternas^*, Orazio Descalzi

^*Corresponding author for this work

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

2 Scopus citations

Abstract

The dynamics of perturbations around sinks and sources of traveling waves (TW) is studied in the cubic-quintic Ginzburg-Landau equation from an analytical point of view. Perturbations generically propagate in a direction opposite to the TW. Thus, a sink of TW is a source of perturbations and vice versa. For small values of time we predict there is a lower bound for the group velocity. For large values of time we predict the asymptotic value of the group velocity of the wave packet. Both predictions are in good agreement with direct numerical simulations.

Original language	English
Pages (from-to)	2821-2826
Number of pages	6
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	17
Issue number	8
DOIs	https://doi.org/10.1142/S0218127407018804
State	Published - Aug 2007

Bibliographical note

Funding Information:
O. Descalzi wishes to thank the support of FAI (Project No. ICIV-001-06), FONDECYT (Project No. 1070098) and Project Anillo en Ciencia y Tec-nología ACT15. J. Cisternas thanks FONDECYT (Project No. 1070098) for financial support.

Keywords

Cubic-quintic Ginzburg-Landau equation
Dissipative dark solitons
Sinks
Sources

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10.1142/S0218127407018804

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title = "Sources and sinks in the vicinity of a weakly inverted instability",

abstract = "The dynamics of perturbations around sinks and sources of traveling waves (TW) is studied in the cubic-quintic Ginzburg-Landau equation from an analytical point of view. Perturbations generically propagate in a direction opposite to the TW. Thus, a sink of TW is a source of perturbations and vice versa. For small values of time we predict there is a lower bound for the group velocity. For large values of time we predict the asymptotic value of the group velocity of the wave packet. Both predictions are in good agreement with direct numerical simulations.",

keywords = "Cubic-quintic Ginzburg-Landau equation, Dissipative dark solitons, Sinks, Sources, Cubic-quintic Ginzburg-Landau equation, Dissipative dark solitons, Sinks, Sources",

author = "Jaime Cisternas and Orazio Descalzi",

note = "Funding Information: O. Descalzi wishes to thank the support of FAI (Project No. ICIV-001-06), FONDECYT (Project No. 1070098) and Project Anillo en Ciencia y Tec-nolog{\'i}a ACT15. J. Cisternas thanks FONDECYT (Project No. 1070098) for financial support.",

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language = "English",

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AU - Cisternas, Jaime

AU - Descalzi, Orazio

N1 - Funding Information: O. Descalzi wishes to thank the support of FAI (Project No. ICIV-001-06), FONDECYT (Project No. 1070098) and Project Anillo en Ciencia y Tec-nología ACT15. J. Cisternas thanks FONDECYT (Project No. 1070098) for financial support.

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N2 - The dynamics of perturbations around sinks and sources of traveling waves (TW) is studied in the cubic-quintic Ginzburg-Landau equation from an analytical point of view. Perturbations generically propagate in a direction opposite to the TW. Thus, a sink of TW is a source of perturbations and vice versa. For small values of time we predict there is a lower bound for the group velocity. For large values of time we predict the asymptotic value of the group velocity of the wave packet. Both predictions are in good agreement with direct numerical simulations.

AB - The dynamics of perturbations around sinks and sources of traveling waves (TW) is studied in the cubic-quintic Ginzburg-Landau equation from an analytical point of view. Perturbations generically propagate in a direction opposite to the TW. Thus, a sink of TW is a source of perturbations and vice versa. For small values of time we predict there is a lower bound for the group velocity. For large values of time we predict the asymptotic value of the group velocity of the wave packet. Both predictions are in good agreement with direct numerical simulations.

KW - Cubic-quintic Ginzburg-Landau equation

KW - Dissipative dark solitons

KW - Sinks

KW - Sources

KW - Cubic-quintic Ginzburg-Landau equation

KW - Dissipative dark solitons

KW - Sinks

KW - Sources

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JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 8

ER -

Sources and sinks in the vicinity of a weakly inverted instability

Abstract

Bibliographical note

Keywords

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