Formation, stability, and dynamics of vector bright solitons in a trapless Bose-Einstein condensate with spin-orbit coupling

We consider a binary self-attractive Bose-Einstein condensate with Rashba spin-orbit coupling in two-dimensional free space. The formation, stability, and dynamics of vector bright solitons are elucidated through numerical analysis and variational approximation. It is found that dynamically stabilized vector bright solitons can be formed in two-dimensional free space with appropriate parameters and ramp schemes, and its motional trajectory and stability show nontrivial behavior and strong dependence on the direction of the force generated by the spin-orbit coupling. Finally, the case of the periodic modulation of spin-orbit coupling is discussed, and an experimental protocol is also given.