Title: Kinematic vortices in a thin film driven by an applied current
Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and an applied magnetic field directed orthogonal to the film. Through a center manifold reduction we develop a rigorous bifurcation theory for the appearance of periodic solutions in certain parameter regimes near the normal state. The leading order dynamics, based on the behavior of the first eigenfunction to a PT-symmetric operator taking the form of a purely imaginary perturbation of the magnetic Schrodinger operator, yield in particular a motion law for kinematic vortices moving up and down the center line of the sample. We also present computations that reveal the co-existence and periodic evolution of kinematic and magnetic vortices.