Working from an integrable two-component (coupled Gross-Pitaevskii) model with constant spin-orbit and Rabi couplings and a time-dependent harmonic trap and scattering length, the paper uses the Darboux transformation with a nontrivial seed to construct exact rogue-wave, breather, mixed rogue-dark-bright, and classical dark-bright soliton solutions. Its distinctive results are the explicit control the two couplings exert on these structures (spin-orbit coupling drives rapid amplitude oscillations of the rogue waves, Rabi coupling produces stripes in the temporal direction) and the demonstration that the rogue-wave instability triggered by an expulsive transient trap can be completely suppressed by tuning the scattering length through a Feshbach resonance.
In this paper, based on an integrable model governed by four system parameters, namely, spin-orbit coupling and Rabi coupling which are constants while the other two parameters, namely the harmonic t…