Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

Details Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

2002-01-25

arxiv.org/abs/nlin/0201047v2

Nonlinearity 15 (2002) 1471-1488

Nonlinear Sciences

Pattern Formation and Solitons

23 pages amslatex, 5 eps figures, minor typos corrected

Scientific paper

10.1088/0951-7715/15/5/307

The time evolution of several interacting Ginzburg-Landau vortices according to an equation of Schroedinger 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.

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