Formation and stability of phase slip centers in nonuniform wires with currents

The problem of phase slip centers in superconducting wires with forced current is studied. It is shown that when the wire is uniform and the temperature and current are in a certain regime in the parameter plane, phase slip centers appear periodically in time at the center of the wire. When the wire is not uniform, the phase slip centers are not stationary, but rather they move through convection by the thickness variation.