  We present a unified description of different types of matter-wave solitons
that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein
condensates (BECs). This description relies on the reduction of the original
two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear
Schr\"{o}dinger equation, via a multiscale expansion method. This way, we find
approximate bright and dark soliton solutions, for attractive and repulsive
interatomic interactions respectively, for different regimes of the SOC
interactions. Beyond this, our approach also reveals "negative mass" regimes,
where corresponding "negative mass" bright or dark solitons can exist for
repulsive or attractive interactions, respectively. Such a unique opportunity
stems from the structure of the excitation spectrum of the SOC-BEC. Numerical
results are found to be in excellent agreement with our analytical predictions.
