The self-action of a Gaussian beam in a cubic medium under conditions of strong nonlinear response of the medium is modeled numerically. It is shown that in the propagation process the beam acquires a close to hyper Gaussian profile, and as the nonlinearity parameter a increases the intensity on the axis of the beam becomes equal to the maximum intensity and for α >5000 the maximum intensity and the intensity on the beam axis do not differ by more than 2%. The efficiency of the calculations performed by the method of splitting and nonlinear difference schemes are compared. It is shown that the self-action of powerful beams is best calculated by using nonlinear schemes combined with Newton's method as implemented in the paper.
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