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

scholarly journals Bound states and interactions of vortex solitons in the discrete Ginzburg-Landau equation

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
C. Mejía-Cortés ◽  
J. M. Soto-Crespo ◽  
Rodrigo A. Vicencio ◽  
Mario I. Molina
Keyword(s):  
Bound States ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Vortex Solitons

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 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.

Stabilization of dark solitons in the cubic Ginzburg-Landau equation

2000 ◽  
Vol 62 (5) ◽  
pp. 7410-7414 ◽  
Author(s):  
N. Efremidis ◽  
K. Hizanidis ◽  
H. E. Nistazakis ◽  
D. J. Frantzeskakis ◽  
B. A. Malomed
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Dark Solitons ◽  
Ginzburg Landau Equation

scholarly journals Some stability results for the complex Ginzburg–Landau equation

2019 ◽  
Vol 22 (08) ◽  
pp. 1950038
Author(s):  
Simão Correia ◽  
Mário Figueira
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Bound States ◽  
Landau Equation ◽  
Strong Solutions ◽  
Ginzburg Landau ◽  
Asymptotic Decay ◽  
Ginzburg Landau Equation ◽  
Stability Results

Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg–Landau equation (CGL), [Formula: see text] with [Formula: see text], are obtained. Moreover, we show the existence of bound-states under certain conditions on the parameters and on the domain. We conclude with the proof of asymptotic stability of these bound-states when [Formula: see text] and [Formula: see text] large enough.

Sign in / Sign up

Export Citation Format

Share Document