Soliton Rectangular Pulses and Bound States in a Dissipative System Modeled by the Variable-Coefficients Complex Cubic-Quintic Ginzburg–Landau Equation

2021 ◽  
Vol 38 (9) ◽  
pp. 094201
Author(s):  
Yuan-Yuan Yan ◽  
Wen-Jun Liu
Keyword(s):  
Bound States ◽  
Landau Equation ◽  
Dissipative System ◽  
Variable Coefficients ◽  
Ginzburg Landau ◽  
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

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 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.

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

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.

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