  The effect of two- and three-body interactions on the modulation instability
(MI) domain formation of a spin-orbit (SO) and Rabi-coupled Bose-Einstein
condensate is studied within a quasi-one-dimensional model. To this aim, we
perform numerical and analytical investigations of the associated dispersion
relations derived from the corresponding coupled Gross-Pitaevskii equation. The
interplay between the linear (SO and Rabi) couplings with the nonlinear
cubic-quintic interactions are explored in the mixture, considering miscible
and immiscible configurations, with a focus on the impact in the analysis of
experimental realizations with general binary coupled systems, in which
nonlinear interactions can be widely varied together with linear couplings.

Quantum Gases