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Abstracts
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.
Discipline
Journal
Year
Volume
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Pages
853-858
Physical description
Dates
published
2007-11
received
2007-09-03
Contributors
author
- 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