Based on the method of separation of variables, a direct approach in the study of soliton perturbations has been developed in our previous paper [Phys. Rev. E 54, 6816 (1996)]. In this paper, we use it to deal with the nonlinear Schr\"odinger and the sine-Gordon equations under the action of perturbations. Results which differ from those in past papers are obtained.
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Tang et al. (1998) studied this question.
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