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

• Published in: Results in physics 2023-08, Vol.51, p.106655, Article 106655
• Main Authors: Belobo Belobo, D., Meier, T.
• Format: Article
• Language: English
• Subjects: Generalized coupled Gross–Pitaevskii equations; Solitary waves; Spin–orbit coupling; Time management of nonlinearities and external potentials
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2023.106655

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. •Explicit solutions of a generalized spin–orbit coupled Gross–Pitaevskii system.•Time variations of external potential and two-body interactions.•Linear potential-induced spatial curvature of and control solitary waves.•Peregrine solitons.•Rogue waves.