Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg–Landau equation with variable coefficients

2006 ◽  
Vol 268 (2) ◽  
pp. 305-310 ◽  
Author(s):  
Fang Fang ◽  
Yan Xiao
Keyword(s):  
Landau Equation ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

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.

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.

Dromion-like structures and stability analysis in the variable coefficients complex Ginzburg–Landau equation

2015 ◽  
Vol 360 ◽  
pp. 341-348 ◽  
Author(s):  
Pring Wong ◽  
Li-Hui Pang ◽  
Long-Gang Huang ◽  
Yan-Qing Li ◽  
Ming Lei ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Landau Equation ◽  
Variable Coefficients ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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