A Fast Compact Difference Method for Two-Dimensional Nonlinear Space-Fractional Complex Ginzburg-Landau Equations

2021 ◽  
Vol 39 (5) ◽  
pp. 697-721
Author(s):  
global LuZhang
Keyword(s):  
Difference Method ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Compact Difference ◽  
Ginzburg Landau Equations ◽  
Compact Difference Method

scholarly journals Finite amplitude convection between stress-free boundaries; Ginzburg–Landau equations and modulation theory

1994 ◽  
Vol 5 (3) ◽  
pp. 267-282 ◽  
Author(s):  
Andrew J. Bernoff
Keyword(s):  
Stability Theory ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Free Boundaries ◽  
Mean Flow ◽  
Onset Of Convection ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Modulation Theory ◽  
The Stability

The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg–Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.

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