Stationary localized solutions in the subcritical complex Ginzburg-Landau equation

O. Descalzi*, M. Argentina, E. Tirapegui

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

The stationary localized solutions in the subcritical complex Ginzburg-Landau equation are studied. It was showed that pulses in the complete quintic one-dimensional Ginzburg-Landau equation with complex coefficients appear through a saddle-node bifurcation which is determined analytically through a suitable approximation of the explicit form of the pulses. The results are in excellent agreement with direct numerical simulations.

Original languageEnglish
Pages (from-to)2459-2465
Number of pages7
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
Issue number11
DOIs
StatePublished - Nov 2002

Bibliographical note

Funding Information:
E. Tirapegui and O. Descalzi wish to thank Fondo de Ayuda a la Investigacion of the U. de los Andes (Project ICIV-001-02) and FONDECYT (P. 1020374). M. Argentina acknowledges the support from FONDECYT (P. 3000017). We would like to thank Dr. Marcel Clerc (Univer-sidad de Chile) and Prof. Helmut Brand (Uni-versitaet Bayreuth, Germany) for many useful discussions. The numerical simulations have been performed using the software developed in the Institute Nonlineaire de Nice, France. We are indebted to Prof. P. Coullet (Nice) for allowing us to use this software.

Keywords

  • Ginzburg-Landau equation
  • Localized structures
  • Saddle-node bifurcation

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