The $c$-axis charge traveling wave in coupled system of Josephson junctions

We demonstrate a manifestation of the charge traveling wave along the $c$-axis (TW) in current voltage characteristics of coupled Josephson junctions in high-$T_c$ superconductors. The branches related to the TW with different wavelengths are found for the stacks with different number of Josephson junctions at different values of system's parameters. Transitions between the TW branches and the outermost branch are observed. The electric charge in the superconducting layers and charge-charge correlation functions for TW and outermost branches show different behavior with bias current. We propose an experimental testing of the TW branching by microwave irradiation.