Generations of polygonal soliton clusters and fundamental solitons by   radially-azimuthally phase-modulated necklace-ring beams in dissipative   systems
  We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasi-polygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasi-polygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of the basic dynamical scenarios; hence this set is a universal one for the CGL models. 
Yingji He, Dumitru Mihalache, Boris A. Malomed, Yunli Qiu, Zhanxu   Chen, and Yifang Li
physics.optics