We study the dynamical properties of bright-bright solitons in two species Bose-Einstein condensates with the repulsive interspecies interactions under the external harmonic potentials by using a variational approach combined with numerical simulation. It is found that the interactions between bright-bright solitons vary from repulsive to attractive interactions with the increasing of their separating distances. And the bright-bright solitons can be localized at equilibrium positions, different from the periodic oscillation of bright soliton in the single species condensates. Especially, a through-collision is newly observed from the bright-bright solitons collisions with the increasing of the initial velocity. The collisional type of bright-bright solitons, either rebound -or through -collision, depends on the modulation of the initial conditions. These results will be helpful for the experimental manipulating such solitons.PACS (2008)

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.