scholarly journals New Explicit and Exact Traveling Waves Solutions To The Modified Complex Ginzburg Landau Equation

2021 ◽  
Author(s):  
Bienvenue Depelair ◽  
Alphonse Houwe ◽  
Hadi Rezazadeh ◽  
Ahmet Bekir ◽  
Mama Nsangou ◽  
...  
Keyword(s):  
Traveling Waves ◽  
Landau Equation ◽  
Transformation Method ◽  
Ginzburg Landau ◽  
Dark Solitons ◽  
Function Transformation ◽  
Ginzburg Landau Equation ◽  
Physical Phenomena

Abstract This paper applies function transformation method to obtain under certain conditions bright, dark, kink and W-shaped dark solitons waves solutions to the modified complex Ginzburg Landau Equation (CGLE). These new obtained solutions can be useful in many applications such as communication, medicine, hydrodynamic, thermodynamic just to name a few and can allow to explain physical phenomena.

Bound states of dark solitons in the quintic Ginzburg-Landau equation

1998 ◽  
Vol 57 (1) ◽  
pp. 1088-1091 ◽  
Author(s):  
V. V. Afanasjev ◽  
P. L. Chu ◽  
B. A. Malomed
Keyword(s):  
Bound States ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Dark Solitons ◽  
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 Bifurcation to traveling waves in the cubic–quintic complex Ginzburg–Landau equation

2015 ◽  
Vol 13 (04) ◽  
pp. 395-411 ◽  
Author(s):  
Jungho Park ◽  
Philip Strzelecki
Keyword(s):  
Traveling Waves ◽  
Landau Equation ◽  
Basic Solution ◽  
Ginzburg Landau ◽  
Center Manifold Reduction ◽  
Modulation Equation ◽  
Ginzburg Landau Equation ◽  
The One ◽  
Manifold Reduction ◽  
Bifurcation And Stability

We consider the one-dimensional complex Ginzburg–Landau equation which is a generic modulation equation describing the nonlinear evolution of patterns in fluid dynamics. The existence of a Hopf bifurcation from the basic solution was proved by Park [Bifurcation and stability of the generalized complex Ginzburg–Landau equation, Pure Appl. Anal. 7(5) (2008) 1237–1253]. We prove in this paper that the solution bifurcates to traveling waves which have constant amplitudes. We also prove that there exist kink-profile traveling waves which have variable amplitudes. The structure of the traveling waves is examined and it is proved by means of the center manifold reduction method and some perturbation arguments, that the variable amplitude traveling waves are quasi-periodic and they connect two constant amplitude traveling waves.

Sign in / Sign up

Export Citation Format

Share Document