PL EN


Preferences help
enabled [disable] Abstract
Number of results
2007 | 112 | 5 | 853-858
Article title

Finding Solitons in Bifurcations of Stationary Solutions of Complex Ginzburg-Landau Equation

Content
Title variants
Languages of publication
EN
Abstracts
EN
Nonlinear dissipative systems, particularly optical dissipative solitons are well described by complex Ginzburg-Landau equation. Solutions of two- and three-dimensional complex cubic-quintic Ginzburg-Landau equation assuming exponential dependence on propagation parameter are studied. Approximate analytical stationary solutions of cubic-quintic Ginzburg-Landau equation are found by solving systems of ordinary differential equations. We are solving two-point boundary problems using adapted shooting method. Stable and unstable branches of the bifurcation diagram are identified using linear stability analysis. In this way we established conditions for generation and propagation of stable dissipative solitons in two and three dimensions. These results are in agreement with numerical simulation of cubic-quintic Ginzburg-Landau equation and the recently established approach based on variational method generalized to dissipative systems and therein established stability criterion.
Keywords
EN
Contributors
  • Institute of Physics, Pregrevica 118, 11001 Belgrade, Serbia
author
  • Laboratoire POMA, UMR 6136 CNRS, University of Angers, 2, Boulevard Lavoisier, 49045 Angers, France
author
  • Laboratoire POMA, UMR 6136 CNRS, University of Angers, 2, Boulevard Lavoisier, 49045 Angers, France
References
  • 1. I. Gabitov, S.K. Turitsyn, Opt. Lett., 21, 327, 1996
  • 2. M. Nakazawa, H. Kubota, Jpn. J. Appl. Phys., 34, L681, 1995
  • 3. N.N. Akhmediev, A.A. Ankiewicz, Solitons, Nonlinear Pulses and Beams, Chapman and Hall, London 1997
  • 4. V. Skarka, V.I. Berezhiani, R. Miklaszewski, Phys. Rev. E, 56, 1080, 1997; V. Skarka, V.I. Berezhiani, R. Miklaszewski, Phys. Rev. E, 59, 1270, 1999
  • 5. V. Skarka, N.B. Aleksic, Phys. Rev. Lett., 96, 013903, 2006
  • 6. N.B. Aleksic, V. Skarka, D.V. Timotijevic, D. Gauthier, Phys. Rev. A, 75, 061802(R), 2007
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv112n520kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.