  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 are 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 construction of
system of the holomorphic nonlinear equations and application of the Newtonian
method for the solution of the nonlinear equations system.
