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[en] We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width by using a perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires a spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively mode-locked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurements in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improvement in the sensitivity and spectroscopic accuracy, which makes soliton absorption spectroscopy a promising measurement technique.