  We analyze the propagation of two-dimensional dispersive and relativistic
wavepackets localized in the vicinity of the zero level set $\Gamma$ of a
domain wall. The main applications we consider are a topologically non-trivial
Dirac model and a similar but topologically trivial Klein-Gordon equation. The
static domain wall models an interface separating two insulating media in
possibly different topological phases. We propose a semiclassical oscillatory
representation of the wavepackets and provide an estimate of their accuracy in
appropriate energy norms. We describe the propagation of relativistic modes
along $\Gamma$ and analyze dispersive modes by a stationary phase method. In
the absence of turning points, we show that arbitrary localized and smooth
initial conditions may be represented as a superposition of such wavepackets.
In the presence of turning points, the results apply only for sufficiently
high-frequency wavepackets.
