Stable spatiotemporal dissipative soliton clusters in the complex Ginzburg-Landau equation

Stable spatiotemporal soliton clusters in the cubic-quintic complex Ginzburg-Landau equation are investigated theoretically. It is revealed that spatiotemporal soliton clusters carrying zero and nonzero topological charges can stably propagate and the clusters don't substantially rotate despite the value of topological charges due to the effect of friction force in such a model. It is found that if the separation of solitons is larger than a critical value, the cluster is maintained, otherwise solitons exhibit too strong an attraction for each other due to being in-phase, which leads to their instability. Prediction of the minimum separation of solitons for bound clusters is demonstrated by use of energy and momentum balance methods.