Stacked long Josephson junctions in zero magnetic field: A numerical study of coupled one-dimensional sine-Gordon equations

We present a systematic numerical study of the coupled one-dimensional sine-Gordon equations for a stack of 20 Josephson junctions, with junction parameters that are representative for intrinsic Josephson junctions in ${\mathrm{Bi}}_2{\mathrm{SrCa}}_2{\mathrm{Cu}}_2{\mathrm{O}}_8.$ Simulations were performed for zero external magnetic field. We found a large variety of fluxon and antifluxon modes, often involving the excitation of collective Josephson plasma oscillations or cavity resonances. Representative states are discussed in detail.