Abstract
Investigation of dynamics of a laser beam in a medium, the dielectric permittivity of which depends on the beam power, represents one of the classical problems of nonlinear physics. In the present paper this problem is solved analytically in the framework of the two-dimensional Schrödinger equation with a focusing cubic nonlinearity and a small defocusing nonlinearity of the fifth order. The model is shown to describe the whole process of stationary self-focusing that spreads along the direction of the beam propagation and consists in decreasing oscillations of the waveguide width. The shape and also the upper and lower envelopes of these oscillations are studied in detail. Parameters of the final state, that is a homogeneous waveguide, are determined.
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