Variational investigation of Gaussian beam propagation in saturable nonlinear media

Propagation of Gaussian beam in a media with saturable nonlinearity is analyzed by using variational approach. The semi-analytical variational method provides a considerable insight on the Gaussian beam dynamic. Furthermore the existence curve of such Gaussian solitons is studied numerically for which can not be evaluated exactly. Numerical results show that Gaussian function is good soliton profile in such media, and the Gaussian beam could propagate stably almost without changing their intensity shape when satisfied the existence curve, otherwise such beam propagate with a periodic or quasi-periodic manner.