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.
Similar content being viewed by others
References
[CE] Collet, P., Eckmann, J.-P.: Instabilities and fronts in extended systems: Princeton, NJ: Princeton University Press 1990
[CEE] Collet, P., Eckmann, J.-P., Epstein, H.: Diffusive repair for the Ginsburg-Landau equation. Helv. Phys. Acta (in press)
[FS] Fabes, E. B., Stroock, D. W.: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Rat. Mech. Anal.96, 327–338 (1986)
[LA] Langer, J. S., Ambegaokar, V.: Intrinsic resistive transition in narrow superconducting channels. Phys. Rev.168, 498–510 (1967)
[M] Moser, J.: On a pointwise estimate for parabolic differential equations. Commun. Pure and Appl. Math.24, 727–740 (1971)
[PW] Protter, M., Weinberger, H.: Maximum principles in partial differential equations. Englewood Cliffs, N.J.: Prentice Hall 1967
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02099141