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Dissipative Optical Solitons

100%
Skarka V., Aleksic N.
Acta Physica Polonica A
|
2007
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vol. 112
|
issue 5
791-798
EN
The generation and nonlinear dynamics of multi-dimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equation. A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of even asymmetric input pulse from this domain leads to stable dissipative solitons and light bullets.
2
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Finding Solitons in Bifurcations of Stationary Solutions of Complex Ginzburg-Landau Equation

81%
Timotijevic D., Derbazi M., Skarka V.
Acta Physica Polonica A
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2007
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vol. 112
|
issue 5
853-858
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.
3
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Stable One-Dimensional Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation

81%
Aleksic N., Pavlovic G., Aleksic B., Skarka V.
Acta Physica Polonica A
|
2007
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vol. 112
|
issue 5
941-947
EN
The generation and nonlinear dynamics of one-dimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the (1+1)-dimensional complex cubic-quintic Ginzburg-Landau equation. A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative temporal solitons. Analytical predictions are confirmed by numerical evolution of input temporal pulses towards stable dissipative solitons.
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