The Dynamics of a Bright–Bright Vector Soliton in Bose–Einstein Condensation

The dynamics of a bright–bright vector soliton in cigar-shaped Bose–Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between the solitons, and may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass center of the system, which will also oscillate harmonically due to harmonic trapping potential.