Solitons interaction in a spherically symmetric Bose–Einstein condensate

By means of modified Poincaré–Lighthill–Kuo (PLK) perturbation method, two spherical solitons and their interaction in a finite sphere-shaped Bose–Einstein condensate with repulsive atomic interactions are investigated. Two spherical Korteweg–de Vries (KdV) equations in the respective reference frames are derived to describe two spherically solitary waves which propagate along the radial direction (one travelling outwards and the other travelling inwards). The spherical soliton solutions and analytical phase shifts after collision are obtained. It is found that the phase shifts strongly depend on the radius of condensate and the initially effective amplitude of soliton. The numerical simulation evidence shows that the phase shift decreases with the radius of condensate and increases with the initial amplitude.