Abstract
We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.
Highlights
Vortices are screw wave front defects that appear in many branches of physics [1, 2, 3]
We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation
Radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters
Summary
Vortices are screw wave front defects that appear in many branches of physics [1, 2, 3]. The requirement of zero field at the center of the beam converts them into ring structures These can exist as exact solutions of nonlinear wave equations. Ring structures in conservative media have been found to be unstable in respect to the modulation instability [25] The result of such instability is usually the filamentation of the beam. In this respect, we should note that the stability properties of vortex solitons in dissipative media [21, 22, 23, 24] are quite different from those in conservative media. Vortex solitons without cylindrical symmetry exist in narrower regions of the parameter space and their shapes vary They remain as a complete ring but acquire a nontrivial azimuthal structure.
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