Manipulation of nonautonomous nonlinear wave solutions of the generalized coupled Gross–Pitaevskii equations with spin–orbit interaction and weak Raman couplings

Using unitary and similarity transformations, explicit solutions of the coupled Gross–Pitaevskii models with spin–orbit coupling and varying nonlinearities and harmonic plus linear potentials are constructed by a mapping to the integrable one-dimensional Manakov system under the constraints of weak Raman coupling and small amplitude waves. An intriguing example for controllability of the dynamics is obtained for the case of a linear potential that induces complex spatial curvatures onto the density profiles. Peregrine solitons are also found demonstrating that the system may sustain rogue waves. It is shown that adiabatic modulations of external potentials and/or two-body atomic interactions may be used to efficiently control the dynamics of the constructed nonlinear waves. Numerical simulations demonstrate the stability of the obtained solutions.