  In this letter we consider the dynamic behaviors of spin-orbit coupled Bose
condensates realized in recent experiments. We show that there exists an
interaction induced ac Hall response which is absent in a non-interacting
system. This condensate has two distinct equilibrium phases known as the plane
wave phase and the stripe phase. In the plane wave phase, we show that an ac
longitudinal current will induce an ac radial current in the transverse
direction, and vice versa, as a cooperation effect of spin-velocity locking and
spin-dependent interaction. In the stripe phase, we show that the dominant
longitudinal response to a transverse radial current is sliding of the density
stripe, because it is the low-lying excitation mode originated from spontaneous
spatial translational symmetry breaking in this phase.
