On the possibility of the observation of the resonance interaction between kinks of the sine-Gordon equation and localized waves in real physical systems

Abstract

The resonance dynamics of kinks of the sine-Gordon equation in a system with a single point impurity with allowance for the generation of localized waves in the presence of an external force and dissipation has been studied. Equations of motion for the coordinate of the kink center and the amplitude of the impurity mode have been found. The analysis of solutions of these equations and results of the numerical simulation of the modified sine-Gordon equation have showed that damping and the external force act against the appearance of the resonance reflection of the kink from the attractive impurity. However, the resonance energy exchange between solitons causing it still takes place.