Perturbation theory for domain walls in the parametric Ginzburg-Landau equation

D.V. Skryabin, A. Yulin, D. Michaelis, W.J. Firth, G.-L. Oppo, U. Peschel, F. Lederer

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Abstract

We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Ising walls, deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion. We then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities.
Original languageEnglish
Article number056618
Number of pages9
JournalPhysical Review E
Volume64
Issue number5
DOIs
Publication statusPublished - 25 Oct 2001

Keywords

  • perturbation theory
  • parametric Ginzburg-Landau equation
  • dynamical properties of domain walls
  • weakly nonlinear theory
  • spatial inhomogeneities

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