Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

O. Lange; B. J. Schroers

doi:10.1088/0951-7715/15/5/307

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Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

O. Lange·B. J. Schroers

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Abstract

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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O. Lange, B. J. Schroers. 2006-02-17. Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices. https://doi.org/10.1088/0951-7715%2F15%2F5%2F307

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