  We consider a class of topological defects in $(1,1)$-dimensions with a
deformed $\phi^4$ kink structure whose stability analysis leads to a
Schr\"odinger-like equation with a zero-mode and at least one vibrational
(shape) mode. We are interested in the dynamics of kink-antikink collisions,
focusing on the structure of two-bounce windows. For small deformation and for
one or two vibrational modes, the observed two-bounce windows are explained by
the standard mechanism of a resonant effect between the first vibrational and
the translational modes. With the increasing of the deformation, the effect of
the appearance of more than one vibrational mode is the gradual disappearance
of the initial two-bounce windows. The total suppression of two-bounce windows
even with the presence of a vibrational mode offers a counterexample from what
expected from the standard mechanism. For even larger deformation, some
two-bounce windows reappear, but with a non-standard structure.

High Energy Physics - Theory