  We find one-, two-, and three-component solitons of the polar and
ferromagnetic (FM) types in the general (non-integrable) model of a spinor
(three-component) model of the Bose-Einstein condensate (BEC), based on a
system of three nonlinearly coupled Gross-Pitaevskii equations. The stability
of the solitons is studied by means of direct simulations, and, in a part,
analytically, using linearized equations for small perturbations. Global
stability of the solitons is considered by means of the energy comparison. As a
result, ground-state and metastable soliton states of the FM and polar types
are identified. For the special integrable version of the model, we develop the
Darboux transformation (DT). As an application of the DT, analytical solutions
are obtained that display full nonlinear evolution of the modulational
instability (MI) of a continuous-wave (CW) state seeded by a small spatially
periodic perturbation. Additionally, by dint of direct simulations, we
demonstrate that solitons of both the polar and FM types, found in the
integrable system, are structurally stable, i.e., they are robust under random
changes of the relevant nonlinear coefficient in time.
