Structured light entities, chaos and nonlocal maps. (original) (raw)
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Abstract
Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. It is shown that Feigenbaum and Ikeda maps may be generalized via inclusion in convolution integrals with kernel in a form of Green function of a relevant linear physical system. It is shown that such iterative nonlocal nonlinear maps are equivalent to nonlinear partial differential equations of Ginzburg-Landau type. Taking kernel as Green functions relevant to generic optical resonators these nonlocal maps emulate the basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing via relaxation oscillations mediated by noise, vortex-antivortex lattices with periodic location of vortex cores. The smooth multimode noise addition facilitates the selection of stable entities and elimination of numerical artifacts.
Publication:
Chaos Solitons and Fractals
Pub Date:
April 2020
DOI:
arXiv:
Bibcode:
Keywords:
- Chaotic maps;
- Integral transforms;
- Solitons;
- Vortices;
- Vortex lattices;
- Turbulence;
- Physics - Optics;
- Nonlinear Sciences - Pattern Formation and Solitons
E-Print:
11 pages, 8 figures,submitted to referred journal