Exact coherent matter-wave soliton induced and controlled by laser field

We find a set of exact solutions of coherent bright solitons in the quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) trapped in a harmonic potential, by using a Gaussian laser well (barrier) with oscillating position to balance the repulsive (attractive) interatomic interaction. The bright solitons do not deform in propagation and are controlled accurately by the laser driving which resonates with the trapping potential. The solitonic motion is more stable for the repulsive BEC than that of the attractive BEC. The results reveal a different kind of soliton trains compared to that reported recently in Phys. Rev. Lett. 100, 164102 (2008) and suggest an experimental scheme for generating and controlling the coherent matter-wave solitons.