Breather—kink-antikink-pair conversion in the driven sine-Gordon system

Breather excitations in the sine-Gordon equation influenced by constant driving forces are investigated—large driving forces cause the breather to split into a $k\bar{k}(2\mathrm{}\pi \mathrm{kink}-2\mathrm{}\pi \mathrm{antikink})$ pair while for small driving forces the breather excitations enter stationary modes. A perturbation method and a potential-energy argument yields expressions for the threshold for breather decomposition. Good agreement between theory and numerical results is found when the initial phase ($\theta$) of the breather is either 0 or $\pi$. For $\theta \cong \frac{\pi }{2}$ and $\theta \cong \frac{3\pi }{2}$ the deviation gets larger.