  We consider the one-dimensional Ising-like fully anisotropic S=1/2 Heisenberg
antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations
in the presence of transverse magnetic field $h_x$. We obtain dynamical spin
correlation functions along the magnetic field $S^{xx}(q,\omega)$ and
perpendicular to it $S^{yy}(q,\omega)$. It is shown that the line shapes of
$S^{xx}(q,\omega)$ and $S^{yy}(q,\omega)$ are purely symmetric at the
zone-boundary. It is observed in $S^{yy}(q,\omega)$ for $\pi/2<q<\pi$ that the
spectral weight moves toward low energy side with the increase of $h_x$. This
model is applicable to study the spin dynamics of CsCoCl$_3$ in the presence of
weak interchain interactions.
