Unstable manifolds and Schrodinger dynamics of Ginzburg-Landau vortices

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Abstract

The time evolution of several interacting Ginzburg-Landau vortices according to an equation of Schrodinger type is approximated by motion on a finite-dimensional manifold. That manifold is defined as an unstable manifold of an auxiliary dynamical system, namely the gradient flow of the Ginzburg-Landau energy functional. For two vortices the relevant unstable manifold is constructed numerically and the induced dynamics is computed. The resulting model provides a complete picture of the vortex motion for arbitrary vortex separation, including well-separated and nearly coincident vortices.
Original languageEnglish
Article numberPII S0951-7715(02)33343-7
Pages (from-to)1471-1488
Number of pages18
JournalNonlinearity
Volume15
Issue number5
DOIs
Publication statusPublished - 15 Jul 2002

Keywords

  • COMPLEX SCALAR FIELDS
  • VORTEX DYNAMICS
  • CAUCHY-PROBLEM
  • LOCAL SPACES
  • EQUATION
  • LAW

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