Matter-wave solitons in a spin-1 Bose-Einstein condensate with time-modulated external potential and scattering lengths

In this paper, we present many matter-wave solitons in a system of three component Gross-Pitaevskii equation arising from the context of spinor Bose-Einstein condensates with time-modulated external potential and scattering lengths. The three component Gross-Pitaevskii equation with time-dependent parameters is first transformed into a three coupled nonlinear Schrödinger equation, then the exact soliton solutions of the three coupled nonlinear Schrödinger equation are given explicitly. Finally, the dynamics of the matter-wave solitons in the F = 1 spinor Bose-Einstein condensates is examined by specially choosing the frequency of the external potential. It is shown that when the frequency of the external potential is constant, there exist different kinds of matter-wave solitons as the atomic s-wave scattering lengths are varied about time, such as solitons with shape changing interactions, two-soliton bound states, squeezed matter-wave solitons, single bright and dark solitons. When the frequency of the external potential is time-modulated, there also exist various matter-wave solitons in the F = 1 spinor Bose-Einstein condensates, and we show that the time evolutions of the matter-wave solitons are sharply changed by the time-dependent trap frequency and nonlinear coefficients