Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation

1994 ◽  
Vol 124 (6) ◽  
pp. 1075-1088 ◽  
Author(s):  
Xinfu Chen ◽  
Charles M. Elliott ◽  
Tang Qi
Keyword(s):  
Real Number ◽  
Shooting Method ◽  
Landau Equation ◽  
Stationary Solutions ◽  
Polar Coordinates ◽  
Ginzburg Landau ◽  
Nonzero Constant ◽  
Ginzburg Landau Equation ◽  
Vortex Solutions ◽  
Complex Valued

In this paper, we study all the stationary solutions of the form u(r)einθ to the complex-valued Ginzburg–Landau equation on the complex plane: here (r, θ) are the polar coordinates, and n is any real number. In particular, we show that there exists a unique solution which approaches to a nonzero constant as r → ∞.

PERIODIC NUCLEATION SOLUTIONS OF THE REAL GINZBURG–LANDAU EQUATION IN A FINITE BOX

2002 ◽  
Vol 12 (10) ◽  
pp. 2219-2228 ◽  
Author(s):  
M. ARGENTINA ◽  
O. DESCALZI ◽  
E. TIRAPEGUI
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Landau Equation ◽  
Plane Waves ◽  
Periodic Boundary Conditions ◽  
Stationary Solutions ◽  
Stable Plane ◽  
Ginzburg Landau ◽  
The Real ◽  
Ginzburg Landau Equation

We study the stationary solutions of the real Ginzburg–Landau equation with periodic boundary conditions in a finite box. We show explicitly how to construct nucleation solutions allowing transitions between stable plane waves.

Sign in / Sign up

Export Citation Format

Share Document