Uniform asymptotic of solution of the cubic nonlinear Schrodinger equation in the focal area of the narrow 2-dimensional focused light beam

The paper is devoted to the study of the diffraction of a two-dimensional narrow focused light beam propagating through the matter whose dielectrical permeability depends on the intensity of a transversal component of the electrical field. It is well known that this process may be described with satisfactory precision by nonlinear Schrodinger equation (NS) with cubic nonlinear part.