Transmission and stability of solitary pulses in complex Ginzburg-Landau equations with variable coefficients

Kwok Wing Chow, Chun Kit Lam, Kaliyaperumal Nakkeeran, Boris Malomed

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

A class of complex Ginzburg-Landau (CGL) equations with variable coefficients is solved exactly by means of the Hirota bilinear method. Two novel features, elaborated in recent works on the bilinear method, are incorporated. One is a modified definition of the bilinear operator, which has been used to construct pulse, hole and front solutions for equations with constant coefficients. The other is the usage of time- or space-dependent wave numbers, which was employed to handle nonlinear Schrodinger (NLS) equations with variable coefficient. One-soliton solutions of the CGL equations with variable coefficients are obtained in an analytical form. A restriction imposed by the method is that the coefficient of the second-order dispersion must be real. However, nonlinear, loss (or gain) is permitted. A simple example of an exponentially modulated dispersion profile is worked out in detail to illustrate the principle. The competition between the linear gain and nonlinear loss, and vice versa, is investigated. The analytical solutions for solitary pulses are tested in direct simulations. The amplified pulses are very robust, provided that the linear gain is reasonably small. The results may be implemented in soliton fiber lasers.

Original languageEnglish
Article number054001
Number of pages5
JournalJournal of the Physical Society of Japan
Volume77
Issue number5
DOIs
Publication statusPublished - 15 May 2008

Keywords

  • cubic complex Ginzburg-Landau equation
  • Hirota method
  • dissipative solitons
  • nonlinear Schrodinger-equation
  • dispersion-decreasing fiber
  • group-velocity dispersion
  • optical-fiber
  • solitons
  • propagation
  • systems
  • gain
  • compression
  • media

Cite this

Transmission and stability of solitary pulses in complex Ginzburg-Landau equations with variable coefficients. / Chow, Kwok Wing; Lam, Chun Kit; Nakkeeran, Kaliyaperumal; Malomed, Boris.

In: Journal of the Physical Society of Japan, Vol. 77, No. 5, 054001, 15.05.2008.

Research output: Contribution to journalArticle

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KW - Hirota method

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KW - nonlinear Schrodinger-equation

KW - dispersion-decreasing fiber

KW - group-velocity dispersion

KW - optical-fiber

KW - solitons

KW - propagation

KW - systems

KW - gain

KW - compression

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