Breather scattering by impurities in the sine-Gordon model

We present results on breather-impurity scattering in the sine-Cordon model. We show in detail how the outcome of the scattering depends on the breather's initial velocity, internal oscillation frequency, and phase. In particular, for an attractive impurity a breather can either be trapped by the impurity, pass the impurity, be totally reflected, or break into a kink-antikink pair. For a repulsive impurity, a high-frequency breather behaves like a rigid particle and the scattering result is mainly determined by the breather's initial velocity; the scattering of a low-frequency breather, however, depends on both the breather's initial velocity and phase (it can either pass the impurity or be reflected for a fixed initial velocity but different phases). We demonstrate clearly that the existence of these complex and interesting phenomena is due to the interplay between the breather's internal and its translational degrees of freedom, which become strongly coupled when the breather is near the impurity region.