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Front solutions for the Ginzburg-Landau equation

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Abstract

We prove the existence of front solutions for the Ginzburg-Landau equation

$$\partial _t u(x,t) = \partial _x^2 u(x,t) + (1 - |u(x,t)|^2 )u(x,t)$$

, interpolating between two stationary solutions of the form\(u(x) = \sqrt {1 - q^2 } e^{iqx}\) with different values ofq atx=±∞. Such fronts are shown to exist when at least one of theq is in the Eckhaus-unstable domain.

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Authors and Affiliations

  1. Département de Physique Théorique, Université de Genève, CH-1211, Geneva 4, Switzerland

    J. -P. Eckmann & Th. Gallay

Authors
  1. J. -P. Eckmann
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  2. Th. Gallay
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Communicated by A. Jaffe

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Eckmann, J.P., Gallay, T. Front solutions for the Ginzburg-Landau equation. Commun.Math. Phys. 152, 221–248 (1993). https://doi.org/10.1007/BF02098298

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  • DOI: https://doi.org/10.1007/BF02098298

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