DYNAMICS OF SELF-TRAPPED BEAMS WITH PHASE DISLOCATION IN SATURABLE KERR AND QUADRATIC NONLINEAR MEDIA

We present a detailed stability analysis of one- and two-ring solitary waves with central phase dislocation in self-focusing saturable and q uadratic nonlinear media. Varying parameters, we demonstrate transitio ns between different filamentation scenarios. An analytical approach i s developed for the study of filament dynamics after ring breakup. App roximate expressions for the angular separation rate of filaments base d on the conservation of the angular momentum and on the conservation of the Hamiltonian are derived and competed. Thr stability analysis an d analytical results are tested by an extensive series of numerical si mulations of the original models, and good agreement is found.