Sine-Gordon breathers on spatially periodic potentials

We have carried out an extensive simulation program to study the behavior of sine-Gordon breathers initially at rest in the presence of perturbations that are periodic in space and constant in time. We report here a number of different observed phenomena and the range of the relevant parameters (the ratio of the breather width to the perturbation wavelength and the perturbation magnitude) for which each one of them occurs. We also propose some qualitative explanations valid for certain regimes.