Resonant breather states in Josephson coupled systems

A review of diverse resonant effects appearing in weakly dissipative Josephson coupled systems in the presence of inhomogeneous dynamic localized state (discrete breather) is given. As particular examples I discuss the resonant interaction of breather states with linear electromagnetic excitations (EEs) in dc driven Josephson junction ladders and a single plaquette containing three Josephson junctions. Such resonant interaction manifests itself by resonant steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the resonant interaction leads to an increase of breather dynamical complexity, e.g., enlargement of the breather core, low symmetry or quasiperiodic breather states. I show that the application of an external magnetic field allows to tune the resonant interaction, and correspondingly to increase (or decrease) the height of the resonant steps, to change the stability of the breather states.