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

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