  During defect-antidefect scattering, bound modes frequently disappear into
the continuous spectrum before the defects themselves collide. This leads to a
structural, nonperturbative change in the spectrum of small excitations.
Sometimes the effect can be seen as a hard wall from which the defect can
bounce off. We show the existence of these spectral walls and study their
properties in the $\phi^4$ model with BPS preserving impurity, where the
spectral wall phenomenon can be isolated because the static force between the
antikink and the impurity vanishes. We conclude that such spectral walls should
surround all solitons possessing internal modes.
