Controlling Soliton Collisions of Condensates by Time-Dependence of Both Interactions and External Potential

Considering time-dependence of both interactions and external potential,we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation.It is found that for a closed external potential,the soliton-soliton distance is decreased with nonlinearly increased interactions,while the amplitude of each soliton increases and its width decreases.For linearly increased interactions but nonlinearly decreased external potential,especially,the atom transfer between two solitons is observed,different from previous theory of no atom transfer in solitons collision in a fixed external potential.In addition,it is shown that the collisional type,such as head-on,＂chase＂,or collision period between two solitons,can be controlled by tuning both interactions and external potential.The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.