  We derive classes of exact solitonic solutions of the time-dependent
Gross-Pitaevskii equation with repulsive and attractive interatomic
interactions. The solutions correspond to a string of bright solitons with
phase difference between adjacent solitons equal to $\pi$. While the relative
phase, width, and distance between adjacent solitons turn out to be a constant
of the motion, the center of mass of the string moves with a constant
acceleration arising from the inhomogeneity of the background.
