Modulation instability of solutions to the complex Ginzburg-Landau equation

Branislav N. Aleksić; Najdan B. Aleksić; Vladimir Skarka; Milivoj R. Belić

doi:10.1088/0031-8949/2014/T162/014002

Modulation instability of solutions to the complex Ginzburg-Landau equation

Branislav N. Aleksić^*, Najdan B. Aleksić, Vladimir Skarka, Milivoj R. Belić

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

The modulation instability of continuous-wave (CW) solutions of the complex Ginzburg-Landau equation (CGLE), with arbitrary intensity-dependent nonlinearity, is studied. The variational approach and standard linear stability analysis are used to investigate the stability of CW and to obtain the criteria for modulation stability in the general form. Analytical stability criteria are established, enabling the construction of charts of stable fixed points of the cubic-quintic CGLE. We show that the evolution of modulationally stable and unstable CWs depends on the CGLE parameters. The analytical predictions for plane wave stability are confirmed by exhaustive numerical simulations.

Original language	English
Article number	014002
Journal	Unknown Journal
Volume	T162
DOIs	https://doi.org/10.1088/0031-8949/2014/T162/014002
Publication status	Published - 1 Sept 2014
Externally published	Yes
Event	4th International School and Conference on Photonics, PHOTONICA 2013 - Belgrade, Serbia Duration: 26 Aug 2013 → 30 Aug 2013

Keywords

complex Ginzburg-Landau equation
continuous wave
modulation instability
stability analysis

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title = "Modulation instability of solutions to the complex Ginzburg-Landau equation",

abstract = "The modulation instability of continuous-wave (CW) solutions of the complex Ginzburg-Landau equation (CGLE), with arbitrary intensity-dependent nonlinearity, is studied. The variational approach and standard linear stability analysis are used to investigate the stability of CW and to obtain the criteria for modulation stability in the general form. Analytical stability criteria are established, enabling the construction of charts of stable fixed points of the cubic-quintic CGLE. We show that the evolution of modulationally stable and unstable CWs depends on the CGLE parameters. The analytical predictions for plane wave stability are confirmed by exhaustive numerical simulations.",

keywords = "complex Ginzburg-Landau equation, continuous wave, modulation instability, stability analysis",

author = "Aleksi{\'c}, {Branislav N.} and Aleksi{\'c}, {Najdan B.} and Vladimir Skarka and Beli{\'c}, {Milivoj R.}",

note = "Publisher Copyright: {\textcopyright} 2014 The Royal Swedish Academy of Sciences Printed in the UK.; 4th International School and Conference on Photonics, PHOTONICA 2013 ; Conference date: 26-08-2013 Through 30-08-2013",

year = "2014",

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doi = "10.1088/0031-8949/2014/T162/014002",

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TY - JOUR

T1 - Modulation instability of solutions to the complex Ginzburg-Landau equation

AU - Aleksić, Branislav N.

AU - Aleksić, Najdan B.

AU - Skarka, Vladimir

AU - Belić, Milivoj R.

PY - 2014/9/1

Y1 - 2014/9/1

N2 - The modulation instability of continuous-wave (CW) solutions of the complex Ginzburg-Landau equation (CGLE), with arbitrary intensity-dependent nonlinearity, is studied. The variational approach and standard linear stability analysis are used to investigate the stability of CW and to obtain the criteria for modulation stability in the general form. Analytical stability criteria are established, enabling the construction of charts of stable fixed points of the cubic-quintic CGLE. We show that the evolution of modulationally stable and unstable CWs depends on the CGLE parameters. The analytical predictions for plane wave stability are confirmed by exhaustive numerical simulations.

AB - The modulation instability of continuous-wave (CW) solutions of the complex Ginzburg-Landau equation (CGLE), with arbitrary intensity-dependent nonlinearity, is studied. The variational approach and standard linear stability analysis are used to investigate the stability of CW and to obtain the criteria for modulation stability in the general form. Analytical stability criteria are established, enabling the construction of charts of stable fixed points of the cubic-quintic CGLE. We show that the evolution of modulationally stable and unstable CWs depends on the CGLE parameters. The analytical predictions for plane wave stability are confirmed by exhaustive numerical simulations.

KW - complex Ginzburg-Landau equation

KW - continuous wave

KW - modulation instability

KW - stability analysis

UR - http://www.scopus.com/inward/record.url?scp=84907298146&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/2014/T162/014002

DO - 10.1088/0031-8949/2014/T162/014002

M3 - Conference article

AN - SCOPUS:84907298146

VL - T162

JO - Unknown Journal

JF - Unknown Journal

M1 - 014002

T2 - 4th International School and Conference on Photonics, PHOTONICA 2013

Y2 - 26 August 2013 through 30 August 2013

ER -

Modulation instability of solutions to the complex Ginzburg-Landau equation

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