Dynamics of vortex singularities in nonlinear PDE

Project description

Nonlinear PDE of Ginzburg-Landau type can be used to model a wide range of phenomena, from ferromagnetic materials and superconductors to quantum field theory. For certain ranges of the Ginzburg-Landau parameter (for self-duality and for point vortices), the equations can be reduced to ODEs. The focus of the present project will be to study the equations of motion in a wider setting, with the aim to extend the range of validity of the reductions and to compare almost singular solutions of the PDEs with simplified ODEs that describe the motion of the singularities. The project will use mostly rigorous analysis and possibly numerical simulation.