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

• Authors: D. Timotijevic , M. Derbazi , V. Skarka
• 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

42.65.Sf; 42.65.Tg

Discipline

• 42.65.Tg: Optical solitons; nonlinear guided waves(for solitons in fibers, see 42.81.Dp)
• 42.65.Sf: Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics

• Journal: Acta Physica Polonica A
• Year: 2007
• Volume: 112
• Issue: 5
• Pages: 853-858

Dates

published

2007-11

received

2007-09-03

Contributors

author

D. Timotijevic

• Institute of Physics, Pregrevica 118, 11001 Belgrade, Serbia

author

M. Derbazi

• Laboratoire POMA, UMR 6136 CNRS, University of Angers, 2, Boulevard Lavoisier, 49045 Angers, France

author

V. Skarka

• Laboratoire POMA, UMR 6136 CNRS, University of Angers, 2, Boulevard Lavoisier, 49045 Angers, France

References

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• 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

Identifiers

DOI

10.12693/APhysPolA.112.853