Stable vortex solitons in the two-dimensional Ginzburg-Landau equation

L. C. Crasovan, B. A. Malomed, D. Mihalache

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Abstract

In the framework of the complex cubic-quintic Ginzburg-Landau equation, we perform a systematic analysis of two-dimensional axisymmetric doughnut-shaped localized pulses with the inner phase field in the form of a rotating spiral. We put forward a qualitative argument which suggests that, on the contrary to the known fundamental azimuthal instability of spinning doughnut-shaped solitons in the cubic-quintic NLS equation, their GL counterparts may be stable. This is confirmed by massive direct simulations, and, in a more rigorous way, by calculating the growth rate of the dominant perturbation eigenmode. It is shown that very robust spiral solitons with (at least) the values of the vorticity (Formula presented) (Formula presented) and (Formula presented) can be easily generated from a large variety of initial pulses having the same values of intrinsic vorticity (Formula presented) In a large domain of the parameter space, it is found that all the stable solitons coexist, each one being a strong attractor inside its own class of localized two-dimensional pulses distinguished by their vorticity. In a smaller region of the parameter space, stable solitons with (Formula presented) and (Formula presented) coexist, while the one with (Formula presented) is absent. Stable breathers, i.e., both nonspiraling and spiraling solitons demonstrating persistent quasiperiodic internal vibrations, are found too.

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