Stable vortex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation

D. Mihalache*, D. Mazilu, F. Lederer, Y. V. Kartashov, L. C. Crasovan, L. Torner, B. A. Malomed

*Corresponding author for this work

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165 Scopus citations


We demonstrate the existence of stable toroidal dissipative solitons with the inner phase field in the form of rotating spirals, corresponding to vorticity S=0, 1, and 2, in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The stable solitons easily self-trap from pulses with embedded vorticity. The stability is corroborated by accurate computation of growth rates for perturbation eigenmodes. The results provide the first example of stable vortex tori in a 3D dissipative medium, as well as the first example of higher-order tori (with S=2) in any nonlinear medium. It is found that all stable vortical solitons coexist in a large domain of the parameter space; in smaller regions, there coexist stable solitons with either S=0 and S=1, or S=1 and S=2.

Original languageEnglish
Article number073904
JournalPhysical Review Letters
Issue number7
StatePublished - 2006


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