- 92-79 Eckmann J.-P., Gallay Th.
- Front solutions for the Ginzburg-Landau equation
Jun 30, 92
(auto. generated ps),
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Abstract. We prove the existence of front solutions
for the Ginzburg-Landau equation
d/dt u(x,t) = d^2/dx^2 u(x,t) + (1 - |u(x,t)|^2) * u(x,t)
interpolating between two stationary solutions of the form
u(x) = sqrt(1 - q^2) * exp(iqx)
with different values of q at x = +-infinity.
Such fronts are shown to exist
when at least one of the q is in the Eckhaus-unstable domain.