English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The propagation of stable coherent entities of an electromagnetic field innonlinear media with parameters varying in space can be described in theframework of iterations of nonlinear integral transformations. It is shown thatfor a set of geometries relevant to typical problems of nonlinear optics,numerical modeling by reducing to dynamical systems with discrete time andcontinuous spatial variables to iterates of local nonlinear Feigenbaum andIkeda mappings and nonlocal diffusion-dispersion linear integral transforms isequivalent to partial differential equations of the Ginzburg-Landau type in afairly wide range of parameters. Such nonlocal mappings , which are theproducts of matrix operators in the numerical implementation, turn out to bestable numerical-difference schemes, provide fast convergence and an adequateapproximation of solutions. The realism of this approach allows one to takeinto account the effect of noise on nonlinear dynamics by superimposing aspatial noise specified in the form of a multimode random process at eachiteration and selecting the stable wave configurations. The nonlinear waveformations described by this method include optical phase singularities,spatial solitons, and turbulent states with fast decay of correlations. Theparticular interest is in the periodic configurations of the electromagneticfield obtained by this numerical method that arise as a result of phasesynchronization, such as optical lattices and self-organized vortex clusters.

Numerical investigation of coherent and turbulent structures of light via nonlinear integral mappings