DYNAMICS OF CIRCULAR ARRAYS OF JOSEPHSON-JUNCTIONS AND THE DISCRETE SINE-GORDON EQUATION

We analyze the damped, driven, discrete sine-Gordon equation with peri odic boundary conditions and constant forcing. Analytical and numerica l results are presented about the existence, stability, and bifurcatio ns of traveling waves in this system. These results are compared with experimental measurements of the current-voltage (I-V) characteristics of a ring of N=8 underdamped Josephson junctions. We find two types o f traveling waves: low-velocity kinks and high-velocity whirling modes . The kinks excite small-amplitude linear waves in their wake. At cert ain drive strengths, the linear waves phase-lock to the kink, generati ng resonant steps in the I-V curve. Steps also occur in the high-veloc ity region, due to parametric instabilities of the whirling mode. We a nalyze the onset of these instabilities, then numerically study the se condary bifurcations and complex spatiotemporal phenomena that occur p ast the onset. In all cases, the measured voltage locations of the res onant steps are in good agreement with the predictions.