Fluxon-antifluxon annihilation in the perturbed sine-Gordon equation with loss and driving terms is investigated. For the infinite line we find a simple analytic expression for the threshold driving term corresponding to annihilation. With the application of the results to a Josephson junction of finite length an expression for the current voltage characteristic of a zero-field step is derived. The analytical results are in good agreement with numerical simulations. The method is extendable to other systems.
Physical Review B, 1984, Vol 30, Issue 7, p. 4057-4059