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We consider a binary self-attractive Bose–Einstein condensate with Rashba spin–orbit coupling (SOC) in two-dimensional (2D) 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 2D 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 SOC. Finally, the case of the periodic modulation of SOC is discussed, and an experimental protocol is also given.

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