Stability of dark soliton solutions of the quintic complex Ginzburg–Landau equation in the case of normal dispersion

2006 ◽  
Vol 15 (11) ◽  
pp. 2638-2643 ◽  
Author(s):  
Tang Zheng-Hua ◽  
Yan Jia-Ren ◽  
Liu Ling-Hong
Keyword(s):  
Landau Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Ginzburg Landau ◽  
Normal Dispersion ◽  
Ginzburg Landau Equation

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 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.

Exact homoclinic wave and soliton solutions for the 2D Ginzburg–Landau equation

2008 ◽  
Vol 372 (17) ◽  
pp. 3010-3014 ◽  
Author(s):  
Zhengde Dai ◽  
Zitian Li ◽  
Zhenjiang Liu ◽  
Donglong Li
Keyword(s):  
Landau Equation ◽  
Soliton Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

Generalized Differential Transform Method for Solving Discrete Complex Cubic Ginzburg–Landau Equation

2015 ◽  
Vol 12 (03) ◽  
pp. 1550017 ◽  
Author(s):  
H. Aminikhah ◽  
P. Dehghan
Keyword(s):  
Solitary Wave Solution ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Differential Transform Method ◽  
Transform Method ◽  
Ginzburg Landau ◽  
Differential Transform ◽  
Generalized Differential ◽  
Discrete Complex

In this paper, generalized differential transform method (GDTM) is applied to solve discrete complex cubic Ginzburg–Landau (DCCGL) equation which is a famous nonlinear difference-differential equation (NDDE). GDTM approximate solutions for various discrete soliton solutions of DCCGL such as discrete bright soliton, discrete dark soliton, and discrete alternating soliton are obtained. Also this method is successfully employed to obtain approximate solution for dark solitary wave solution of integrable discrete nonlinear Schrödinger (IDNS) equation. Numerical results compared with their corresponding numerical and analytical solutions to show the efficiency and high accuracy of the considered method.

Sign in / Sign up

Export Citation Format

Share Document