Direct Approach Based on the Separation of Variables for the Soliton Study of Perturbed Sine-Gordon Equation

A new direct approach based on the separation of variables for the study of soliton perturbations is developed.As an example,the effects of perturbation on a soliton(kink),i.e.,both the time-dependence of soliton parameters and the first-order correction are derived for perturbed sine-Gordon equation.Our approach is very concise and easy to understand,and it can be extended directly to deal with other nonlinear evolution equations.