  Two effectively one-dimensional parallel coupled Bose-Einstein condensates in
the presence of external potentials are studied. The system is modelled by
linearly coupled Gross-Pitaevskii equations. In particular, the interactions of
grey-soliton-like solutions representing analogues of superconducting Josephson
fluxons as well as coupled dark solitons are discussed. A theoretical
approximation based on variational formulations to calculate the oscillation
frequency of the grey-soliton-like solution is derived and a qualitatively good
agreement is obtained.
