New solutions in the theory of self-focusing with saturating nonlinearity

On the basis of an approximate analytic solution of a Cauchy problem for a nonlinear Schrödinger (NLS) equation describing steady-state light beams in a medium with saturating nonlinearity by the method of renormgroup (RG) symmetries, a classification of self-focusing solutions is given depending on two control parameters: the relative contributions of diffraction and nonlinearity and the saturation strength of the nonlinearity. The existence of tube-type self-focusing solutions is proved for an entering beam with Gaussian radial distribution of intensity. Numerical simulation is carried out that allows one to verify the theory developed and to determine its applicability limits.