In-plane fluxon in layered superconductors with arbitrary number of layers

The a shape of an in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) is studied analytically and numerically both in static and dynamic cases. An approximate analytic fluxon solution for stacks with an arbitrary number of layers, junction parameters, and interlayer coupling is derived. For the stack of N junctions, the fluxon is characterized by N spatial components. The fluxon shape strongly depends on N. With increasing N, the phase/current and the magnetic field of the fluxon decouple from each other. Even more unusual is the shape of the fluxon in the dynamic state. Pure solitonic fluxon motion exists up to the lowest characteristic velocity of individual components, c₁. As the velocity of the fluxon approaches c₁, the direction of the current in neighboring junctions starts altering. At velocities above c₁, the fluxon motion is accompanied by ``Cherenkov'' radiation. The spectrum of such radiation may consist of several Josephson plasma modes, which originate from the degenerated fluxon components. For comparison with real-high-T_c superconducting samples, large-scale numerical simulations with up to 600 SJJ's and with in-plane lengths up to 4000 λ_J, are presented.