Rytov transformation in the problem of the self-focusing of a light beam

A method of the complex phase of the envelope of a light field has been proposed for the problem of the self-focusing of a beam in a medium with cubic nonlinearity. The complex phase has been introduced by means of the Rytov transformation. Boundary conditions have been obtained under the assumption that the light fields at the periphery of the beam undergoing self-focusing and linear diffraction coincide with each other. The transition from the slowly varying amplitude to its complex phase provides a significant expansion of the ranges of the amplitude and intensity in the light beam in theoretical investigations. The applicability of the complex phase method is illustrated on particular examples.