Analytical results for the fluxon-antifluxon annihilation process in Josephson junctions

The perturbation theory for the velocity of fluxons moving on a Josephson line has been extended to junctions of finite length. This is done by including the energy loss during collisions, the bias input energy, and the phase-shift experienced by a soliton approaching a boundary. This enables us to calculate approximate dc IV-characteristics of inline and overlap junctions. These are compared to full numerical simulations. In addition a simple expression for the soliton annihilation curve is given.