Non-autonomous bright-dark solitons and Rabi oscillations in multi-component Bose-Einstein condensates (Q2873626)

Recently, many works have been dealing with various complex models in optics and Bose-Einstein condensation, aiming to explicitly transform specially designed versions of the corresponding complex equations to known integrable equations. In the present work, this approach is applied to systems of two and three coupled one-dimensional nonlinear Schrödinger equations, which are considered as Gross-Pitaevskii equations for binary and spinor Bose-Einstein condensates, including a time-dependent trapping potential, a time-dependent coefficient of the self-repulsive nonlinearity, and the Rabi coupling (linear mixing) between the two components. The system is designed in a special form which admits a direct transformation to the integrable Manakov's system. Then, using known exact solutions of the latter system, and transforming those solutions back to the original notation, exact solutions for the original system are produced, which describe the dynamics of a single soliton and collisions between two solitons. The analysis is performed for two formats of the time modulation of the nonlinearity coefficient: kink-like and time-periodic. In the three-component system, collisions between solitons in the presence of the Rabi coupling lead to interesting outcomes, such as mutual switchings between dark and bright components of dark-bright solitons.