  We theoretically study the motion of a magnetic domain wall induced by
transverse elastic waves in a one-dimensional magnetic wire, which respects
both rotational and translational symmetries. By invoking the conservation of
the associated total angular and linear momenta, we are able to derive the
torque and the force on the domain wall exerted by the waves. We then show how
ferromagnetic and antiferromagnetic domain walls can be driven by circularly-
and linear-polarized waves, respectively. We envision that elastic waves may
provide effective means to drive the dynamics of magnetic solitons in
insulators.
