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Dissipative ring solitons with vorticity
J M Soto-Crespo1, N Akhmediev, C Mejia-Cortés
1Instituto de Optica, C.S.I.C., Serrano 121, 28006 Madrid, Spain. jsoto@io.cfmac.csic.es
Optics Express
|March 19, 2009
Summary
Dissipative ring solitons in complex Ginzburg-Landau equations can remain stable and maintain topological charge even after losing radial symmetry. Bifurcations lead to complex, stable, non-circular soliton states.
Area of Science:
- Nonlinear physics
- Optical solitons
- Complex Ginzburg-Landau equations
Background:
- Dissipative systems support stable localized structures.
- Ring solitons in (2+1) dimensions are of significant interest.
- Vorticity and topological charge are key parameters in soliton dynamics.
Purpose of the Study:
- Investigate the stability and dynamics of dissipative ring solitons with vorticity.
- Explore symmetry breaking and bifurcations in these soliton solutions.
- Characterize the parameter ranges for stable non-radially symmetric solitons.
Main Methods:
- Numerical simulations of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation.
- Analysis of soliton stability by examining parameter-dependent bifurcations.
- Characterization of soliton symmetry and dynamics.
Main Results:
- Radially symmetric ring solitons with any vorticity 'm' are stable within a specific parameter range.
- Beyond stability regions, solitons lose radial symmetry but can remain stable with conserved topological charge.
- Bifurcations lead to n-fold bending symmetry and (m+1)-fold modulation, transforming ring solitons into pulsating or chaotic states.
Conclusions:
- Dissipative ring solitons exhibit rich symmetry-breaking dynamics.
- Stable, non-radially symmetric soliton states exist.
- Topological charge is conserved through various bifurcations, leading to complex soliton behaviors.
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