  We investigate the dynamics around an obstacle potential moving in the
plane-wave state of a pseudospin-$1/2$ Bose-Einstein condensate with Rashba
spin-orbit coupling. We numerically investigate the dynamics of the system and
find that it depends not only on the velocity of the obstacle but also
significantly on the direction of obstacle motion, which are verified by a
Bogoliubov analysis. The excitation diagram with respect to the velocity and
direction is obtained. The dependence of the critical velocity on the strength
of the spin-orbit coupling and the size of the obstacle is also investigated.
