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.
- COMPLEX SCALAR FIELDS
- VORTEX DYNAMICS
- LOCAL SPACES
Schroers, B. J., & Lange, O. (2002). Unstable manifolds and Schrodinger dynamics of Ginzburg-Landau vortices. Nonlinearity, 15(5), 1471-1488. [PII S0951-7715(02)33343-7]. https://doi.org/10.1088/0951-7715/15/5/307