  We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons
with equal Rashba and Dresselhaus couplings. The phase diagram of the system is
discussed with special emphasis to the role of the interaction treated in the
mean-field approximation. For a critical value of the density and of the Raman
coupling we predict the occurrence of a characteristic tri-critical point
separating the spin mixed, the phase separated and the single minimum states of
the Bose gas. The corresponding quantum phases are investigated analyzing the
momentum distribution, the longitudinal and transverse spin-polarization and
the emergence of density fringes. The effect of harmonic trapping as well as
the role of the breaking of spin symmetry in the interaction Hamiltonian are
also discussed.
