  We characterize the soliton solutions and their interactions for a system of
coupled evolution equations of nonlinear Schr\"odinger (NLS) type that models
the dynamics in one-dimensional repulsive Bose-Einstein condensates with spin
one, taking advantage of the representation of such model as a special
reduction of a 2 x 2 matrix NLS system. Specifically, we study in detail the
case in which solutions tend to a non-zero background at space infinities.
First we derive a compact representation for the multi-soliton solutions in the
system using the Inverse Scattering Transform (IST). We introduce the notion of
canonical form of a solution, corresponding to the case when the background is
proportional to the identity. We show that solutions for which the asymptotic
behavior at infinity is not proportional to the identity, referred to as being
in non-canonical form, can be reduced to canonical form by unitary
transformations that preserve the symmetric nature of the solution (physically
corresponding to complex rotations of the quantization axes). Then we give a
complete characterization of the two families of one-soliton solutions arising
in this problem, corresponding to ferromagnetic and to polar states of the
system, and we discuss how the physical parameters of the solitons for each
family are related to the spectral data in the IST. We also show that any
ferromagnetic one-soliton solution in canonical form can be reduced to a single
dark soliton of the scalar NLS equation, and any polar one-soliton solution in
canonical form is unitarily equivalent to a pair of oppositely polarized
displaced scalar dark solitons up to a rotation of the quantization axes.
Finally, we discuss two-soliton interactions and we present a complete
classification of the possible scenarios that can arise depending on whether
either soliton is of ferromagnetic or polar type.
