Abstract
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.
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