The generation and nonlinear dynamics of multidimensional optical dissipative solitonic pulses are examined. The variational method is extended to complex dissipative systems, in order to obtain steady state solutions of the $(D+1)$-dimensional complex cubic-quintic Ginzburg-Landau equation ($D=1,2,3$). A stability criterion is established fixing a domain of dissipative parameters for stable steady state solutions. Following numerical simulations, evolution of any input pulse from this domain leads to stable dissipative solitons.

• Received 17 August 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.013903