scholarly journals New findings for the old problem: Exact solutions for domain walls in coupled real Ginzburg-Landau equations

2021 ◽  
pp. 127802
Author(s):  
Boris A. Malomed
Keyword(s):  
Exact Solutions ◽  
Domain Walls ◽  
Ginzburg Landau ◽  
New Findings ◽  
Ginzburg Landau Equations

scholarly journals Exact Solutions for Domain Walls in Coupled Complex Ginzburg–Landau Equations

2011 ◽  
Vol 80 (6) ◽  
pp. 064001 ◽  
Author(s):  
Tat Leung Yee ◽  
Alan Cheng Hou Tsang ◽  
Boris Malomed ◽  
Kwok Wing Chow
Keyword(s):  
Exact Solutions ◽  
Domain Walls ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

Exact solutions of generalized Zakharov and Ginzburg–Landau equations

2007 ◽  
Vol 32 (5) ◽  
pp. 1877-1886 ◽  
Author(s):  
Jin-Liang Zhang ◽  
Ming-Liang Wang ◽  
Ke-Quan Gao
Keyword(s):  
Exact Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

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