Solitons and their collisions in the spinor Bose-Einstein condensates

Under investigation in this paper is a system of three-component Gross-Pitaevskii equations, which can describe the dynamics of F=1 spinor Bose-Einstein condensates in one dimension. By employing the Hirota method and symbolic computation, we obtain the explicit bright one- and two-soliton solutions for the system in the integrable case, which is associated with the attractive mean-field collision and ferromagnetic spin-exchange collision. According to the spin states, we classify the one-soliton solutions into two types: the ferromagnetic and polar solitons. Ferromagnetic solitons in three components share the same pulse shape. Polar solitons in three components have the one- or two-peak profiles, and the separated distance between two peaks is related to the polarization parameters. Based on the asymptotic analysis, collisions between two solitons are discussed in the polar-polar, polar-ferromagnetic, and ferromagnetic-ferromagnetic cases, respectively.