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

Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method