On an explicit method for the numerical solution of problems of light wave propagation in nonlinear media

Attention is given to a method for the numerical solution of problems of axisymmetric-beam propagation in media with positive cubic nonlinearity on the basis of the parabolic-equation approach. A numerical experiment shows that the use of a mobile Lagrangian grid renders explicit methods of numerical solution stable. It is noted that this approach can be used to solve a large number of problems concerning the self-focusing of light beams with different intensity and phase profiles upon entering the nonlinear medium.