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.
Koch, R., & Hill, G. (2016). A millennium of stasis in avian ornamentation? Implications for sexual selection theory. Ideas in Ecology and Evolution. https://doi.org/10.4033/iee.2015.8.13.n