Resonant soliton-impurity interactions

Abstract

We describe a new type of soliton-impurity interaction and demonstrate that the soliton can be totally reflected by an attractive impurity if its initial velocity lies in certain resonance ``windows.'' This effect has an analogy with the resonance phenomena in kink-antikink collisions [Campbell, Schonfeld, and Wingate, Physica (Amsterdam) 9D, 1 (1983)], and it can be explained by a resonant energy exchange between the soliton and the impurity mode. Taking the sine-Gordon and ${\mathrm{\ensuremath{\varphi}}}^{4}$ models as examples, we find a number of resonance windows by numerical simulations and develop a collective-coordinate approach to describe the effect analytically.