Exact Solution of a New Superconducting State

An exact solution of a new superconducting state is obtained which exists for dc currents larger than the critical current in thin wires. The order parameter is zero at all times at certain points in the whisker, thereby permitting the phase to slip at a constant rate, a consequence of which is a dc potential difference between the separate singly connected superconducting regions. These solutions are periodic in space and stable in time and lead to voltage steps in the dc $V-I$ characteristic.