Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium

In this paper we investigate the self-focusing of a Gaussian beam in a saturable nonlinear medium. We show that the dynamics of the incident Gaussian beam become progressively more complicated as the ratio of the Gaussian spot size to that of the ground-state solution is increased for a fixed energy flux. As this ratio is increased (or decreased) from unity, recurrence of the field is observed followed by a mixture of recurrence and azimuthal-symmetry breaking, and finally there is strong azimuthal-symmetry breaking resulting in beam breakup into solitary waves. In this last stage there is no evidence that the field will recur at larger propagation distances.