Soliton localization in disordered one-dimensional Josephson transmission lines

We present a study on the propagation of topological solitons (fluxons) in the strongly nonlinear system of a one-dimensional discrete Josephson transmission line with regions of disorder. Using numerical simulations, the probability of fluxon transmission is calculated stochastically, and in the presence of disorder is found to decay exponentially. The localization length is found to increase sharply with decreasing disorder strength, suggesting that fluxon-solitons may become delocalized below a certain threshold value of disorder. We describe a basic experiment to observe the predicted effects.