A numerical study of the self-similar solutions of the Schroedinger Map
  We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-parameter family, develop a singularity at finite time. We study a number of boundary conditions that allow us reproduce the mechanism of singularity formation. Some related questions are also considered. 
Francisco de la Hoz, Carlos Garcia-Cervera, Luis Vega