Algorithms of the diffraction problem solution of a plane wave on nonlinear dielectric layer

On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on the nonlinear object is shown. The first of them based on the iterative scheme is applicable to the solution of non-homogeneous system of the second kind nonlinear equations. The second algorithm bases on Newtonian method of solution of the nonlinear equations system.