Equation describing the evolution of optical radiation in a nonlinear medium

In the presented work, the transition from the classical system of Maxwell equations to the one-dimensional nonlinear Schrodinger equation is presented, which can be exactly solved by the method of the inverse scattering problem. This equation represents the solution in the form of a spatial soliton. The obtained equations represent a spatial soliton sloping, that in a self-focused medium with cubic nonlinearity, a beam of a continuous medium propagates. Thus, the found solutions represent the fundamental mode of an optical waveguide induced by a propagating beam. (author)