ABSTRACT. Magnetic flux quanta, of value h/2e, in long Josephson junctions behave as (quasi) solitons. Fluxon dynamical states are well described by a perturbed sine-Gordon equation model, with boundary conditions determined by the junction geometry and by externally applied magnetic fields, and they give rise to readily measurable physical phenomena, such as step structure in current-voltage characteristics and microwave radiation emission. Devices based on fluxon propagation offer potentially interesting applications as oscillators and amplifiers-as well as digital applications, described elsewhere in this volume-in high performance integrated superconductive circuits.

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.

We investigate by numerical simulations the behavior of the power dissipated Assuming realistic values for the parameters R and C, both in the high-and in the low-T c case the power is large enough to allow the operation of such a device in applications. 74.50.+r, 85.25.Dq