Numerical research of methods for multidimentional solitons search

Over the last years, along with the development of optical computing systems, the mathematical modeling of laser femtosecond pulses in nonlinear media has been actively developing. Among the proposed methods for finding solitons the most widespread methods are the method of the inverse problem, spectral methods and other methods. The authors present two iterative methods, namely M1 and M2, for finding soliton solutions in the propagation of optical radiation in a medium with a cubic nonlinearity in the axially symmetric case.