Perturbation treatment of boundary conditions for fluxon motion in long Josephson junctions

The sine-Gordon equation governing the motion of fluxons in the long Josephson junction is investigated by transforming it into a relativistic-particle equation of motion and using a perturbational approach. The effects of a finite junction length, an external magnetic field, as well as the effects of fluxon-antifluxon collisions are included in the calculations. All theoretical results are compared to numerical simulations in order to investigate the validity of the approach. Good agreement is found in most cases.