A perturbation theory is developed to investigate the effects of various perturbations on soliton propagation down an optical fiber. The theory is formulated within the «natural» framework of inverse scattering theory. The perturbative effects of third-order dispersion, the soliton self-frequency shift, bandwidth-limited gain, periodic modulation, and stochastic fluctuations are analyzed in detail. In each case, the analytic results presented here are in excellent agreement with simulations carried out here and elsewhere