Vortical nucleation solutions in a model of superflow

Stable and unstable (nucleation) stationary solutions of the non-linear Schrodinger equation, describing super-flow around a disc, are numerically computed. The stable branch and the unstable branch are connected through a saddle-node bifurcation. The unstable branch generates, through a pitchfork bifurcation, solutions that are asymmetric with respect to the diameter of the disc. The symmetric and asymmetric nucleation solutions contain, respectively, two or one vortices that emerge from the disc at sub-critical velocities.