Resonant soliton-impurity interactions

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 ${\mathrm{\phi }}^4$ models as examples, we find a number of resonance windows by numerical simulations and develop a collective-coordinate approach to describe the effect analytically.