Abstract
We consider the Ginsburg-Landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space asx→±∞. If these solutions are not very different, then we show that the initial data will evolve to a stationary solution by a “phase melting” process which avoids “phase slips,” i.e., which does not go through zero amplitude.
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Communicated by A. Jaffe
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Collet, P., Eckmann, J.P. Solutions without phase-slip for the Ginsburg-Landau equation. Commun.Math. Phys. 145, 345–356 (1992). https://doi.org/10.1007/BF02099141
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DOI: https://doi.org/10.1007/BF02099141