Fluxon analogues and dark solitons in linearly coupled BoseEinstein condensates

Two effectively one-dimensional parallel coupled BoseEinstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled GrossPitaevskii equations. In particular, grey-soliton-like solutions representing analogues of superconducting Josephson fluxons as well as coupled dark solitons are discussed. Theoretical approximations based on variational formulations are derived. It is found that the presence of a magnetic trap can destabilize the fluxon analogues. However, stabilization is possible by controlling the effective linear coupling between the condensates.