Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a variational approximation and a numerical solution. Plots of chemical potential and root mean square (rms) size of solitons are obtained for the quasi-one-dimensional model of three different dipolar condensates of 52Cr, 168Er and 164Dy atoms. The results achieved are in good agreement with those produced by the full three-dimensional mean-field model of the condensate. We also study the dynamics of the collision of a train of two solitons in the quasi-one-dimensional model of every condensate above. At small velocities (zero or close to zero) the dynamics is attractive for a phase difference {\delta} = 0, the solitons coalesce and these oscillate forming a bound soliton molecule. For a phase difference {\delta} = {\pi} the effect is repulsive. At large velocities the collision is independent of the initial phase difference {\delta}. This is quasi-elastic and the result is two quasi-solitons.