Gaussian beam propagation in d-dimensional cubic-quintic nonlinear medium

The variational approach has been applied to study the propagation of Gauss ian beams in a medium with d-transverse dimensions and a cubic-quintic nonl inearity. We find implicit conditions for the steady-state propagation and determine the stability of steady-state solutions to symmetric perturbation s. 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 i nitial Gaussian beam with finite radius of curvature into a steady-state be am. The results of the variational approach are congruous with recent numer ical simulations.