Vector dark and bright soliton wave solutions and collisions for spin-1 Bose-Einstein condensate

We hereby work on the generalized three-coupled Gross-Pitaevskii equations by means of the Darboux transformation and Hirota's method. By modulating the external trap potential, atom gain or loss, and coupling coefficients, we can obtain several nonautonomous matter-wave solitons including dark-dark-dark and bright-bright-bright shapes. Propagation and interaction behaviors of the nonautonomous vector solitons are analyzed through the one- and two-soliton solutions. Then, the managements and dynamic behaviors of these solutions are investigated analytically, such as the snaking behaviors, parabolic behaviors and interaction behaviors. Interactions between the linear-type, parabolic-type and periodic-type dark and bright two solitons are elastic. The results could be of interest in such diverse fields as Bose-Einstein condensates and nonlinear fibers.