We consider in-line and overlap geometry models of Josephson junctions with point or rectangular inhomogeneity and investigate the effect of their location on the Josephson vortices and the current. We analyze numerically the critical dependencies "current-magnetic field" caused by one- and two-point current injections. The obtained results elucidate the relation between these critical curves and the fractions of the injection current at the ends of the junction. We also find out similarities between the exponentially shaped junctions, and those with inhomogeneity at the end when a two-point current injection is present. We juxtapose the critical curves of the distinct junctions with inner inhomogeneity and discuss the similarity between them and the Josephson junctions with phase shifts. The transitions of Josephson junctions from a superconducting mode to a resistive one as bifurcations of the static solutions of appropriately posed multiparametric compound boundary- and eigenvalue problems are interpreted and solved using the continuous analog of Newton method.
Effect of ordered array of magnetic dots on the dynamics of Josephson vortices in stacked SNS Josephson junctions under DC and AC current
