Mathematical modeling of filamentation processes in the medium with a cubic nonlinearity

In the thesis the problem of intensive laser beam propagation in the medium with a cubic nonlinearity is considered. The choice of mathematical models and adequate algorithms is investigated, partially, the choice of optimal grids and difference schemes for the mathematical modeling of filamentation processes. On the basis of paraxial approximation and the Bespalov–Talanov theory of the plane wave instability the results have been received both for filaments and their interaction. The mathematical modeling of the filamentation regimes has shown that the Bespalov–Talanov theory describes the initial stage of the instability with high accuracy. It is established that the approach of filaments on the plane wave background may influence the wave evolution in a different way depending on their parameters.