Synthetic spin-orbit (SO) coupling, an important ingredient for quantum simulation of many exotic condensed matter physics, has recently attracted considerable attention. The static and dynamic properties of a SO coupled Bose-Einstein condensate (BEC) have been extensively studied in both theory and experiment. Here we numerically investigate the generation and propagation of a textit{dynamical} spin-density wave (SDW) in a SO coupled BEC using a fast moving Gaussian-shaped barrier. We find that the SDW wavelength is sensitive to the barriers velocity while varies slightly with the barriers peak potential or width. We qualitatively explain the generation of SDW by considering a rectangular barrier in a one dimensional system. Our results may motivate future experimental and theoretical investigations of rich dynamics in the SO coupled BEC induced by a moving barrier.
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