  We consider a binary Bose-Einstein condensate with linear and nonlinear
interactions between its components, which emulate the spinor system with
spin-orbit (SO) and Rabi couplings. For a relatively dense condensate, 1D
coupled equations with the nonpolynomial nonlinearity of both repulsive and
attractive signs are derived from the 3D Gross-Pitaevskii equations. Profiles
of modes confined in an external potential under the action of the
self-repulsion, and self-trapped solitons in the case of the self-attraction,
are found in a numerical form and by means of analytical approximations. In the
former case, the interplay of the SO and Rabi couplings with the repulsive
nonlinearity strongly distorts shapes of the trapped modes, adding conspicuous
side lobes to them. In the case of the attractive nonlinearity, the most
essential result is reduction of the collapse threshold under the action of the
SO and Rabi couplings.
