Bunched fluxons in coupled Josephson junctions

Abstract

The nature of bunched fluxons on coupled long Josephson junctions is investigated theoretically by means of a coupled set of sine-Gordon equations. For cases of inductive and capacitive coupling between the junctions, we analyze the stability of the bunched states for different velocities and perturbation parameters, damping and bias. The internal oscillation frequency is found for the bunched modes and the origin of the stability is discussed for the different types of bound states. Extensive numerical simulations are carried out in order to validate the analytical results against the dynamical behavior of the full system. Excellent agreement between the analysis and the simulations is obtained for all values of coupling parameters and velocities. Finally, we demonstrate numerically that the stability of the bound states can persist even when the two systems are not exactly identical, and we conclude that both inductive and capacitive coupling can give rise to large-locking regimes in synchronization experiments on coupled Josephson junctions.