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 $S=0,$ $1,$ and $2$ can be easily generated from a large variety of initial pulses having the same values of intrinsic vorticity $S.\mathrm{}$ 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 $S=1\mathrm{}$ and $2$ coexist, while the one with $S=0\mathrm{}$ is absent. Stable breathers, i.e., both nonspiraling and spiraling solitons demonstrating persistent quasiperiodic internal vibrations, are found too.

• Received 19 June 2000

DOI:https://doi.org/10.1103/PhysRevE.63.016605