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 derived the Green's function corresponding to approximation equations of different orders. Finally, we obtained the effects of perturbation on a soliton, namely both the slow time dependence of the soliton parameters and the corrections up to the second-order approximation. The higher-order effects can also be obtained in the same way.