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Nonautonomous matter waves in a spin-1 Bose-Einstein condensate.

To investigate nonautonomous matter waves with time-dependent modulation in a one-dimensional trapped spin-1 Bose-Einstein condensate, we hereby work on the generalized three-coupled Gross-Pitaevskii equations by means of the Hirota bilinear method. By modulating the external trap potential, atom gain or loss, and coupling coefficients, we can obtain several nonautonomous matter-wave solitons and rogue waves including "bright" and "dark" shapes and arrive at the following conclusions: (i) the external trap potential and atom gain or loss can influence the propagation of matter-wave solitons and the duration and frequency of bound solitonic interaction, but they have little effect on the head-on solitonic interaction; (ii) through numerical simulation, stable evolution of the matter-wave solitons is realized with a perturbation of 5% initial random noise, and the spin-exchange interaction of atoms can be affected by the time-dependent modulation; (iii) under the influence of a periodically modulated trap potential and periodic atom gain or loss, rogue waves can emerge in the superposition of localized character and periodic oscillating properties.