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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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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
PubMed
Summary
This summary is machine-generated.

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.

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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.