  We study matter-wave bright solitons in spin-orbit (SO) coupled Bose-Einstein
condensates (BECs) with attractive interatomic interactions. We use a
multiscale expansion method to identify solution families for chemical
potentials in the semi-infinite gap of the linear energy spectrum. Depending on
the linear and spin-orbit coupling strengths, the solitons may resemble either
standard bright nonlinear Schr\"{o}dinger solitons or exhibit a modulated
density profile, reminiscent of the stripe phase of SO-coupled repulsive BECs.
Our numerical results are in excellent agreement with our analytical findings,
and demonstrate the potential robustness of such solitons for experimentally
relevant conditions through stability analysis and direct numerical
simulations.
