Weak and strong solutions of the complex Ginzburg-Landau equation

1994 ◽  
Vol 71 (3) ◽  
pp. 285-318 ◽  
Author(s):  
Charles R Doering ◽  
John D Gibbon ◽  
C David Levermore
Keyword(s):  
Landau Equation ◽  
Strong Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Weak And Strong Solutions

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.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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