Collisional phase shifts of ring dark solitons in inhomogeneous Bose–Einstein condensates

Abstract

Abstract The head-on collisions of two ring dark solitons in inhomogeneous Bose–Einstein condensates (BECs) with thin disk-shaped potential are studied by the extended Poincare–Lighthill–Kuo (PLK) perturbation method. The result shows 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 two modified cylindrical KdV equations in the respective reference frames. In particular, the analytical phase shifts induced by the head-on collisions between two ring dark solitary waves are derived, and the result shows that the phase shifts change with the radial coordinate r according to the ( 1 + σ r 2 ) r − 1 / 3 law (where σ ∼ ω r 2 / ω z 2 ), which are quite different with the homogeneous case.