scholarly journals Long time behaviour for generalized complex Ginzburg–Landau equation

2007 ◽  
Vol 330 (2) ◽  
pp. 934-948 ◽  
Author(s):  
Donglong Li ◽  
Zhengde Dai ◽  
Xuhong Liu
Keyword(s):  
Landau Equation ◽  
Time Behaviour ◽  
Ginzburg Landau ◽  
Long Time Behaviour ◽  
Ginzburg Landau Equation ◽  
Generalized Complex ◽  
Long Time

Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers

2017 ◽  
Vol 89 (4) ◽  
pp. 2933-2939 ◽  
Author(s):  
Wenjun Liu ◽  
Weitian Yu ◽  
Chunyu Yang ◽  
Mengli Liu ◽  
Yujia Zhang ◽  
...  
Keyword(s):  
Fiber Lasers ◽  
Landau Equation ◽  
Analytic Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Generalized Complex

scholarly journals A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1238 ◽  
Author(s):  
Xiaowei Chen ◽  
Mingzhan Song ◽  
Songhe Song
Keyword(s):  
Energy Dissipation ◽  
Discrete System ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
New Energy ◽  
Long Time ◽  
Space Discretization ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.

Long-time behaviour of Ginzburg-Landau vortices

Nonlinearity ◽  
1998 ◽  
Vol 11 (5) ◽  
pp. 1295-1309 ◽  
Author(s):  
Yu N Ovchinnikov ◽  
I M Sigal
Keyword(s):  
Time Behaviour ◽  
Ginzburg Landau ◽  
Long Time Behaviour ◽  
Long Time
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