Exact analytical solutions of three-dimensional Gross–Pitaevskii equation with time–space modulation

By the generalized sub-equation expansion method and symbolic computation, this paper investigates the (3+1)-dimensional Gross–Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. As a result, rich exact analytical solutions are obtained, which include bright and dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic function solutions. With computer simulation, the main evolution features of some of these solutions are shown by some figures. Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.