Multisoliton Dynamics in the Sine-Gordon Model with Two Point Impurities

Collective variables method is used to derive a set of differential equations to describe the dynamics of a kink in the sine-Gordon model with two identical point impurities taking damping into account. It is shown that the scenarios of kink interaction with the waves localized on the impurities, found from the reduced model, are similar to those obtained earlier by numerical integration of the continuous sine-Gordon equation. For the case of the kink passage through the region with the impurities, the structure and properties of the arising on impurities long-lived four-kink multisolitons are analyzed. For the approximate analytical description of the two bound impurity-localized nonlinear waves, the system of differential equations for harmonic oscillators with elastic link is obtained. The analytical model qualitatively reproduces the results of the sine-Gordon equation numerical simulation. The cases of large and small distances between impurities are analyzed. The results of our study uncover new features of the kink-impurity interaction which is important for a number of applications where the sine-Gordon model is used.