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

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.

Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method

2022 ◽  
Vol 155 ◽  
pp. 111748
Author(s):  
Ahmed H. Arnous ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
Qin Zhou ◽  
Wenjun Liu ◽  
...  
Keyword(s):  
Landau Equation ◽  
Optical Soliton ◽  
Ginzburg Landau ◽  
Soliton Perturbation ◽  
Ginzburg Landau Equation

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.

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.

scholarly journals Optical soliton solutions of the Ginzburg-Landau equation with conformable conformable derivative and Kerr law nonlinearity

2018 ◽  
Vol 65 (1) ◽  
pp. 73 ◽  
Author(s):  
Francisco Gomez ◽  
Behzad Ghanbari
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Ginzburg Landau ◽  
Kerr Law ◽  
Ginzburg Landau Equation ◽  
Kerr Law Nonlinearity ◽  
Exponential Rational Function Method

By using the generalized exponential rational function method we obtain new periodic and hyperbolic soliton solutions for the conformable Ginzburg-Landau equation with Kerr law nonlinearity. The conformable derivative was considered to obtain the exact solutions under constraint conditions. To determine the solution of the model, the method uses the generalization of the exponential rational function method. Numerical simulations are performed to confirm the efficiency of the proposed method.

scholarly journals Non-autonomous Ginzburg-Landau solitons using the He-Li mapping method

2020 ◽  
Vol 27 (4) ◽  
pp. e104
Author(s):  
Maximino Pérez Maldonado ◽  
Haret C. Rosu ◽  
Elizabeth Flores Garduño
Keyword(s):  
Landau Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Mapping Method ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

We find and discuss the non-autonomous soliton solutions in the case of variable nonlinearity and dispersion implied by the Ginzburg-Landau equation with variable coefficients. In this work we obtain non-autonomous Ginzburg-Landau solitons from the standard autonomous Ginzburg-Landau soliton solutions using a simplified version of the He-Li mapping. We find soliton pulses of both arbitrary and fixed amplitudes in terms of a function constrained by a single condition involving the nonlinearity and the dispersion of the medium. This is important because it can be used as a tool for the parametric manipulation of these non-autonomous solitons.

Optical soliton perturbation with complex Ginzburg–Landau equation using trial solution approach

Optik ◽  
2018 ◽  
Vol 160 ◽  
pp. 44-60 ◽  
Author(s):  
Anjan Biswas ◽  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Houria Triki ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Landau Equation ◽  
Optical Soliton ◽  
Ginzburg Landau ◽  
Trial Solution ◽  
Solution Approach ◽  
Soliton Perturbation ◽  
Ginzburg Landau Equation
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