Three-dimensional dissipative optical solitons

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Dumitru Mihalache
Keyword(s):  
Landau Equation ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Optical Solitons ◽  
Ginzburg Landau ◽  
Systematic Analysis ◽  
Dissipative Solitons ◽  
Existence Domain ◽  
Existence And Stability ◽  
The Stability

AbstractA brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane.

Quasi-three dimensional analysis of global instabilities: onset of vortex shedding behind a wavy cylinder

2011 ◽  
Vol 677 ◽  
pp. 572-588 ◽  
Author(s):  
A. GARBARUK ◽  
J. D. CROUCH
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Vortex Shedding ◽  
Eigenvalue Problems ◽  
Landau Equation ◽  
Three Dimensional ◽  
Maximum Diameter ◽  
Ginzburg Landau ◽  
The Stability

In this paper the global-stability theory is extended to account for weak spanwise-flow variations using a quasi-three-dimensional framework. The analysis considers the onset of vortex shedding behind a circular cylinder with a spanwise-varying diameter. The quasi-three-dimensional approach models the fully three-dimensional flow structure as a series of two-dimensional eigenvalue problems representing the sectional-flow behaviour. The sectional results are coupled together using the Ginzburg–Landau equation, which models the diffusive coupling and provides the global response. The onset of global instability (and thus vortex shedding) is linked to both the sectional growth rates (characterized by the maximum-diameter location) and the spanwise extent of the zone of instability. Unsteady numerical simulations are used to guide the global-stability analysis and to assess the fidelity of the predictions. Results from the stability analysis are shown to be in good agreement with the numerical simulations, which are in close agreement with experiments.

scholarly journals Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results

Photonics ◽  
2021 ◽  
Vol 8 (9) ◽  
pp. 353 ◽  
Author(s):  
Boris A. Malomed
Keyword(s):  
Light Propagation ◽  
Inverse Fourier Transform ◽  
Landau Equation ◽  
Optical Solitons ◽  
Variational Approximation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Dissipative Solitons ◽  
Spatial Derivatives ◽  
Derivatives Of

The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schrödinger equation (NLSE) including fractional one-dimensional or two-dimensional diffraction and cubic or cubic-quintic nonlinear terms, as well as linear potentials. The fractional diffraction is represented by fractional-order spatial derivatives of the Riesz type, defined in terms of the direct and inverse Fourier transform. In this form, it can be realized by spatial-domain light propagation in optical setups with a specially devised combination of mirrors, lenses, and phase masks. The results presented in the article were chiefly obtained in a numerical form. Some analytical findings are included too, in particular, for fast moving solitons and the results produced by the variational approximation. Moreover, dissipative solitons are briefly considered, which are governed by the fractional complex Ginzburg–Landau equation.

scholarly journals Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 202 ◽  
Author(s):  
Chen Yue ◽  
Dianchen Lu ◽  
Muhammad Arshad ◽  
Naila Nasreen ◽  
Xiaoyong Qian
Keyword(s):  
Dynamical Equation ◽  
Landau Equation ◽  
Applied Physics ◽  
Ginzburg Landau ◽  
Open Set ◽  
Trigonometric Function Solutions ◽  
Kink Waves ◽  
Mathematical Techniques ◽  
The Stability ◽  
Complex Phenomena

In this paper, bright-dark, multi solitons, and other solutions of a (3 + 1)-dimensional cubic-quintic complex Ginzburg–Landau (CQCGL) dynamical equation are constructed via employing three proposed mathematical techniques. The propagation of ultrashort optical solitons in optical fiber is modeled by this equation. The complex Ginzburg–Landau equation with broken phase symmetry has strict positive space–time entropy for an open set of parameter values. The exact wave results in the forms of dark-bright solitons, breather-type solitons, multi solitons interaction, kink and anti-kink waves, solitary waves, periodic and trigonometric function solutions are achieved. These exact solutions have key applications in engineering and applied physics. The wave solutions that are constructed from existing techniques and novel structures of solitons can be obtained by giving the special values to parameters involved in these methods. The stability of this model is examined by employing the modulation instability analysis which confirms that the model is stable. The movements of some results are depicted graphically, which are constructive to researchers for understanding the complex phenomena of this model.

scholarly journals Optical solitons with differential group delay for complex Ginzburg–Landau equation

2020 ◽  
Vol 16 ◽  
pp. 102888 ◽  
Author(s):  
Yakup Yıldırım ◽  
Anjan Biswas ◽  
Anwar Ja’afar Mohamad Jawad ◽  
Mehmet Ekici ◽  
Qin Zhou ◽  
...  
Keyword(s):  
Group Delay ◽  
Landau Equation ◽  
Optical Solitons ◽  
Differential Group Delay ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Differential Group
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