  The propagation of stable coherent entities of an electromagnetic field in
nonlinear media with parameters varying in space can be described in the
framework of iterations of nonlinear integral transformations. It is shown that
for a set of geometries relevant to typical problems of nonlinear optics,
numerical modeling by reducing to dynamical systems with discrete time and
continuous spatial variables to iterates of local nonlinear Feigenbaum and
Ikeda mappings and nonlocal diffusion-dispersion linear integral transforms is
equivalent to partial differential equations of the Ginzburg-Landau type in a
fairly wide range of parameters. Such nonlocal mappings , which are the
products of matrix operators in the numerical implementation, turn out to be
stable numerical-difference schemes, provide fast convergence and an adequate
approximation of solutions. The realism of this approach allows one to take
into account the effect of noise on nonlinear dynamics by superimposing a
spatial noise specified in the form of a multimode random process at each
iteration and selecting the stable wave configurations. The nonlinear wave
formations described by this method include optical phase singularities,
spatial solitons, and turbulent states with fast decay of correlations. The
particular interest is in the periodic configurations of the electromagnetic
field obtained by this numerical method that arise as a result of phase
synchronization, such as optical lattices and self-organized vortex clusters.
