Direct approach for soliton perturbations based on the Green's function

A direct approach has been developed for soliton perturbations based on the Green's function. We first linearized the soliton equation, and then deriv ed the Green's function corresponding to approximation equations of differe nt orders. Finally, we obtained the effects of perturbation on a soliton, n amely both the slow time dependence of the soliton parameters and the corre ctions up to the second-order approximation. The higher-order effects can a lso be obtained in the same way.