Sine-Gordon2π-kink dynamics in the presence of small perturbations

The influence of external driving forces on the $2\pi$-kink solution to the sine-Gordon equation is examined. The analysis is based on the approach that the solution to the problem can be divided into a $2\pi$-kink part and a background or vacuum part. The behavior of the $2\pi$ kink depends strongly on the initial state of the vacuum. Excellent agreement between the analysis and numerical solution of representative initial-value problems is found.