  In the present study the interaction of a sine-Gordon kink with a localized
inhomogeneity is considered. In the absence of dissipation, the inhomogeneity
considered is found to impose a potential energy barrier. The motion of the
kink for near-critical values of velocities separating transmission from
barrier reflection is studied. Moreover, the existence and stability properties
of the kink at the relevant saddle point are examined and its dynamics is found
to be accurately captured by effective low-dimensional models. In the case
where there is dissipation in the system, below the threshold value of the
current, a stable kink is found to exist in the immediate vicinity of the
barrier. The effective particle motion of the kink is investigated obtaining
very good agreement with the result of the original field model. Both one and
two degree-of-freedom settings are examined with the latter being more
efficient than the former in capturing the details of the kink motion.
