Dynamics of Matter-Wave Solitons for Three-Dimensional Bose–Einstein Condensates with Time-Space Modulation

By two direct assumption methods and symbolic computation, we present two families of one-soliton solutions and a family of two-soliton solutions with some arbitrary functions for the three-dimensional Gross–Pitaevskii equation with time-space modulation. Then we investigate the dynamics of these matter-wave solitons in three-dimensional Bose–Einstein condensates. We can see that the intensities of both one-solitons and two-solitons first increase rapidly to the condensation peak value, then decay very slowly to the background value. Thus these matter-wave solitons in three-dimensional Bose–Einstein condensates can remain for a sufficiently long time to be fully observed and modulated for real applications in today's experiments.