Controlled nonautonomous matter–wave solitons in spinor Bose–Einstein condensates with spatiotemporal modulation

To study controlled evolution of non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation, we focus on a system three coupled Gross-Pitaevskii (GP) equations space-time-dependent external potentials and temporally modulated gain/loss distributions. An integrability condition non-isospectral Lax pair for the GP are obtained. Using it, derive an infinite set dynamical invariants, first two which mass momentum. The Darboux transform is used to generate one- two-soliton solutions. Under action different distributions, various solutions both ferromagnetic polar types obtained, such as self-compressed, snake-like stepwise solitons, well breathers. In particular, formation states resembling rogue waves, under sign-reversible gain-loss distribution, demonstrated too. Shape-preserving changing interactions between bound addressed this context, spin switching arises polar-ferromagnetic interaction. Stability verified by means systematic simulations their perturbed evolution.