Perturbation theory for the kink of the sine-gordon equation

Abstract

A singular perturbation theory is developed to investigate the kink propagating in systems governed by the sine-Gordon equation with perturbations. The outstanding characteristic of the present theory lies in that the dynamic equation and the dispersive wave as well as the "translation mode" are consistently determined in a natural manner, involving no sophisticated derivations pertaining to the inverse scattering transform. A distinct and strict linearization for the subject is introduced. Some notable cases are reformulated by the theory.