scholarly journals Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 219
Author(s):  
Khalil S. Al-Ghafri
Keyword(s):  
Differential Equation ◽  
Optical Fibers ◽  
Power Law ◽  
Elliptic Function ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Space Time ◽  
Optical Soliton ◽  
Ginzburg Landau ◽  
Weierstrass Elliptic Function

In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.

Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media

2020 ◽  
Vol 34 (19) ◽  
pp. 2050179
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Fiber Optics ◽  
Optical Fibers ◽  
Landau Equation ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Power Laws ◽  
Optical Soliton ◽  
Quantum Plasma ◽  
Ginzburg Landau ◽  
Soliton Dynamics

In this research article, our aim is to construct new optical soliton solutions for nonlinear complex Ginzburg–Landau equation with the help of modified mathematical technique. In this work, we studied both laws of nonlinearity (Kerr and power laws). The obtained solutions represent dark and bright solitons, singular and combined bright-dark solitons, traveling wave, and periodic solitary wave. The determined solutions provide help in the development of optical fibers, soliton dynamics, and nonlinear optics. The constructed solitonic solutions prove that the applicable technique is more reliable, efficient, fruitful and powerful to investigate higher order complex nonlinear partial differential equations (PDEs) involved in mathematical physics, quantum plasma, geophysics, mechanics, fiber optics, field of engineering, and many other kinds of applied sciences.

Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

2021 ◽  
Author(s):  
Marco A. Viscarra ◽  
Deterlino Urzagasti
Keyword(s):  
Optical Fibers ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Two Dimensions ◽  
Ginzburg Landau ◽  
Normal Dispersion ◽  
Homogeneous Solutions ◽  
Dark Solitons ◽  
Ginzburg Landau Equation

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

scholarly journals The complex Ginzburg Landau equation in kerr and parabolic law media

2020 ◽  
Vol 10 (1) ◽  
pp. 113-117
Author(s):  
Esma Ates
Keyword(s):  
Landau Equation ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Jacobi Elliptic Function ◽  
Paper Study ◽  
Ansatz Method ◽  
Ginzburg Landau ◽  
Parabolic Law ◽  
Ginzburg Landau Equation ◽  
Existence Criteria

This paper study the complex Ginzburg-Landau equation with two different forms of nonlinearity. The Jacobi elliptic ansatz method is used to obtain the optical soliton solutions of this equation in the kerr and parabolic law media. Bright and dark optical soliton solutions are acquired as well as Jacobi elliptic function solutions. The existence criteria of these solutions are also indicated.

scholarly journals Bright, dark, and singular optical soliton solutions for perturbed Gerdjikov-Ivanov equation

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 151-156
Author(s):  
Esma Ulutas ◽  
Mustafa Inc ◽  
Dumitru Baleanu ◽  
Sunil Kumar
Keyword(s):  
Exact Solutions ◽  
Optical Fibers ◽  
Elliptic Function ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Optical Soliton ◽  
Jacobi Elliptic Function ◽  
Jacobi Elliptic Functions ◽  
Ansatz Method ◽  
Pulse Dynamics

This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.

scholarly journals New optical soliton solutions via generalized Kudryashov’s scheme for Ginzburg–Landau equation in fractal order

2021 ◽  
Vol 60 (6) ◽  
pp. 5495-5510
Author(s):  
Loubna Ouahid ◽  
Saud Owyed ◽  
M.A. Abdou ◽  
Nawal A. Alshehri ◽  
S.K. Elagan
Keyword(s):  
Landau Equation ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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