Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.045803· OSTI ID:21020858

Mihalache, D; Mazilu, D ^[1]; Lederer, F ^[2]; Leblond, H ^[3]; Malomed, B A ^[4]

---

1. Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125 (Romania)
2. Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universitaet Jena, Max-Wien-Platz 1, D-077743 Jena (Germany)
3. Laboratoire POMA, UMR 6136, Universite d'Angers, 2 Bd Lavoisier, 49000 Angers (France)
4. Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We complete the stability analysis for three-dimensional dissipative solitons with intrinsic vorticity S in the complex Ginzburg-Landau equation with cubic and quintic terms in its dissipative and conservative parts. It is found and qualitatively explained that a necessary stability condition for all vortex solitons, but not for the fundamental ones (S=0), is the presence of nonzero diffusivity in the transverse plane. The fundamental solitons are stable in all cases when they exist, while the vortex solitons are stable only in a part of their existence domain. However, the spectral filtering (i.e., the temporal-domain diffusivity) is not necessary for the stability of any species of dissipative solitons. In addition to the recently studied solitons with S=0,1,2, a stability region is also found for ones with S=3.

• OSTI ID: 21020858
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
EQUATIONS
GINZBURG-LANDAU THEORY
NONLINEAR PROBLEMS
SOLITONS
STABILITY
THREE-DIMENSIONAL CALCULATIONS
VORTICES