92-79 Eckmann J.-P., Gallay Th.

Front solutions for the Ginzburg-Landau equation (376K, postscript) Jun 30, 92

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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.

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