  We present a class of three-dimensional solitary waves solutions of the
Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein
condensates (BECs). By imposing an external controlling potential, a desired
time-dependent shape of the localized BEC excitation is obtained. The stability
of some obtained localized solutions is checked by solving the time-dependent
GP equation numerically with analytic solutions as initial conditions. The
analytic solutions can be used to design external potentials to control the
localized BECs in experiment.
