Resonances in nonlinear Klein-Gordon kink scattering by impurities

Abstract

The scattering of topological kinks by point-like impurities is numerically studied in the framework of the sine-Gordon and φ ⁴ models. In the first case, we show that previous approximate analytical results are indeed applicable. Thus, for low velocities, the reflection coefficient depends oscillatorily on the distance between impurities, i.e., resonant scattering takes place. On the other hand, this effect disappears for higher velocities. This result is found to hold also for the φ ⁴ model nonlinearly coupled to the impurities, whereas the linear coupling for the same model gives rise to a different behaviour.