Abstract
The variational approach has been applied to study the propagation of Gaussian beams in a medium with d-transverse dimensions and a cubic-quintic nonlinearity. We find implicit conditions for the steady-state propagation and determine the stability of steady-state solutions to symmetric perturbations. In some parameter regime the stationary beam is stable and leads to the formation of light-bullets. We have also investigated the evolution of an initial Gaussian beam with finite radius of curvature into a steady-state beam. The results of the variational approach are congruous with recent numerical simulations.
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