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By using the Crank–Nicolson method, we investigate numerically the dynamical properties of bright–bright solitons in two species Bose–Einstein condensates (BECs) trapped in an optical lattice. We confirm that the soliton splitting behavior occurs at a critical depth of optical potential. The splitting behavior of solitons and the fusion behavior of condensates can be accurately controlled by adjusting the depth and lattice parameter of optical potential, the initial amplitude and position of solitons, and the interspecies interactions. When the lattice parameter is fixed but the interspecies interaction increased exponentially with the time, each soliton splits into two soltions with different amplitude, and partial fusion of two species BECs can be found. While the interspecies interaction remains unchanged but the lattice parameter increases exponentially with the time, interestingly, the bright solitons with zero initial velocity can pass through each other and accomplish a transmission collision. Furthermore, for the case of both the interspecies interaction and lattice parameter increased exponentially with the time, a head-on collision of the bright solitons in two species BECs occurred. After the collision, each soliton splits into two soltions with equal amplitude. Meanwhile, the complete fusion of two species BECs can be observed. The relevant results can provide help for the precise manipulation of BECs experiments.

The controlled fission, fusion and collision behavior of two species Bose–Einstein condensates with an optical potential