Structured light entities, chaos and nonlocal maps

  title={Structured light entities, chaos and nonlocal maps},
  author={A. Yu Okulov},
  journal={Chaos Solitons \& Fractals},
  • A. Okulov
  • Published 26 January 2019
  • Physics
  • Chaos Solitons & Fractals
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… Expand
3 Citations

Figures from this paper

Observation of the rotational Doppler shift of the ring Airy Gaussian vortex beam
Abstract We observe the rotational Doppler shift of an orbital angular momentum-carrying ring Airy Gaussian vortex (RAiGV) beam based on the rotational Doppler effect (RDE) for the first time. TheExpand


Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management.
The variational approximation with rational and hyperbolic trial functions is used to transform this NLSE into Hamiltonian dynamical systems which give rise to chaotic solutions, and the presence of chaos in the variational solutions is corroborated by calculating their power spectra and the correlation dimension of the Poincaré maps. Expand
Discrete vortex solitons.
Localized states in the discrete two-dimensional (2D) nonlinear Schrödinger equation is found: vortex solitons with an integer vorticity S and it is demonstrated that the soliton's vortsicity may be conserved as a dynamical invariant. Expand
Existence and stability of PT-symmetric states in nonlinear two-dimensional square lattices
Abstract Solitons and vortices symmetric with respect to simultaneous parity ( P ) and time reversing ( T ) transformations are considered on the square lattice in the framework of the discreteExpand
Chaotic advection near a three-vortex collapse.
The anomalous properties of tracer statistics are the result of the complex structure of the advection phase space, in particular, of strong stickiness on the boundaries between the regions of chaotic and regular motion. Expand
Nonlinear quantum piston for the controlled generation of vortex rings and soliton trains
We propose a simple way to generate nonlinear excitations in a controllable way by managing interactions in Bose-Einstein condensates. Under the action of a quantum analog of a classical piston, theExpand
Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity
We complete the stability analysis for three-dimensional dissipative solitons with intrinsic vorticity $S$ in the complex Ginzburg-Landau equation with cubic and quintic terms in its dissipative andExpand
Pattern formation outside of equilibrium
A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. ExamplesExpand
Nonstationary vortex lattices in large-aperture class B lasers
Large-aperture class A lasers emit stationary patterns (square vortex lattices) close to the laser threshold. We show that in class B lasers the emitted patterns are in general nonstationary. TheExpand
3D-vortex labyrinths in the near field of solid-state microchip laser
The usage of vortex-labyrinth fields and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98–2.79 µm. The square vortexExpand
Nonlinear Random Waves
Contents: Introduction Linear Random Waves. Some Basic Results Exactly Solvable Models Direct Perturbation Methods From Inverse Scattering to Perturbative Approach Dynamical Solitons under RandomExpand