  We discover that the way spin-waves exert magnetic torques in multiferroic
materials can cause not only domain wall motion, but also magnetization
dynamics for homogeneous magnetization textures. Interestingly, the domain wall
motion can be controlled via purely electrical means with the spin-waves being
generated by an ac electric field $E$ while the direction of the wall motion
also is sensitive to an applied dc $E$ field. Moreover, we determine the
interaction between spin-transfer torque from an electric current and a
magnetic domain wall in multiferroics and show that the Walker breakdown
threshold scales with the magnitude of a perpendicular electric field, offering
a way to control the properties of domain wall propagation via electric gating.
