scholarly journals Two-dimensional solitary pulses in driven diffractive–diffusive complex Ginzburg–Landau equations

2002 ◽  
Vol 167 (3-4) ◽  
pp. 123-135 ◽  
Author(s):  
Hidetsugu Sakaguchi ◽  
Boris A Malomed
Keyword(s):  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

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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