  We study the collision of a kink and an antikink with the excited vibrational
mode in the double sine-Gordon model. The vibrational energy of the wobbling
kinks can turn into translational energy after the collision. This creates
one-bounce as well as a rich structure of higher-bounce resonance windows that
depend on the wobbling phase is in or out of phase at the collision, and the
wobbling amplitude is sufficiently large. This structure of one- and
higher-bounce windows are observed for a wide range of the model's parameters.
We estimated the center of the one-bounce windows using a simple analytical
approximation for the wobbling evolution. The kinks' final wobbling frequency
is Lorentz contracted, which is simply derived from our equations. We also
report that the maximum value of the energy density always has a smooth
behavior in the resonance windows.
