Stability analysis of fundamental dissipative Ginzburg-Landau solitons

In this paper, a stability analysis of the Ginzburg-Landau system is performed using a variational method. Growth rates for radially symmetric (isotropic) and asymmetric (anisotropic) perturbations of fundamental steady-state solutions of the cubic-quintic Ginzburg-Landau equation are found. The stability domain of fundamental dissipative solitons is established. Analytical results are confirmed by exhaustive numerical simulations. (paper)