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

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 Poincaré-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.

Spatial weak-light ring soliton in self-assembled quantum dots

By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ-type three-level self-assembled quantum dots. It is found that this system can exhibit the transparency, and the width of the transparency window becomes wider with the increase of control light field. Interestingly, a weak probe light beam can form spatial weak-light dark solitons. When it propagates along the axial direction, the soliton will transform into a steady spatial weak-light ring dark soltion. In addition, the stability of two-dimensional spatial optical solitons is testified numerically.

Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin–orbit coupled Bose–Einstein condensate

We consider the dynamics and formation of vortices from ring dark solitons in a two-dimensional Bose–Einstein condensate with the Rashba spin–orbit coupling based on the time-dependent coupled Gross–Pitaevskii equation.Compared with previous results,the system exhibits complex dynamical behaviors in the presence of the spin–orbit coupling.With the modulation of the spin–orbit coupling,not only the lifetime of ring dark solitons is greatly prolonged,but also their attenuation kinetics is significantly affected.For two shallow ring dark solitons with the equal strength of the spin–orbit coupling,the radius of ring dark solitons increases to a maximum value over time and then shrinks into a minimum value.Due to the effect of the snake instability,ring dark solitons split into a series of ring-like clusters of vortex pairs,which perform complex oscillations.This indicates that the system is strongly dependent on the presence of the spin–orbit coupling.Furthermore,the effect of different initial modulation depths on the dynamics of ring dark solitons is investigated.