Exact solutions of the sine-Gordon equation describing oscillations in a long (but finite) Josephson junction

Abstract

Readily evaluated exact solutions of the sine-Gordon equation are presented for nonlinear standing-wave oscillations on a fixed length of a lossless Josephson transmission line with open-circuit boundary conditions at the ends. Three distinct species of standing waves are described: (i) plasma oscillation, (ii) breather oscillation, and (iii) fluxon oscillation. Fluxon oscillations can absorb power from an external source of bias current; for this case the volt-ampere characteristics relating bias current to average junction have been computed.