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Two dimensional nonlinear Schrodinger type equations with saturable or non-saturable nonlinearities are studied numerically as models of the self-focussing of a high power laser beam in different media. Transverse Gaussian incident intensity profiles are handled by using Cartesian rather than cylindrical coordinates. Variation in the azimuthal direction is permitted. In the case of a saturable nonlinearity the beam can develop both a ring structure and self-focussed filaments. In contrast collapse rather than filamentation takes place for the non-saturable nonlinearity.
Konno et al. (Sat,) studied this question.