Head-on collision of ring dark solitons in Bose–Einstein condensates

Abstract

The ring dark solitons and their head-on collisions in a Bose–Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincare–Lighthill–Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r−1/3 law and depend on the initial soliton amplitude and radius.