Fluxon propagation and DC current singularities in long Josephson junctions

The current singularities in the d.c. current-voltage characteristics of long Josephson junctions can be interpreted in terms of fluxon propagation. A steady state propagating solution of a mathematical model consisting of the sine-Gordon equation with an added parabolic loss term and a constant current bias term correctly predicts the voltage spacing and the order of magnitude amplitudes of these singularities. Further analysis is indicated to explain the detailed amplitudes, the voltage cutoff for the singularity series, and the internal fine structure observed with real junctions and in mechanical and numerical simulations.