Abstract
A perturbation theory for the MNLS equation with corrections based upon the inverse scattering transform is applied to the description of soliton evolution in the presence of permanent perturbation. In the case of a simple pole of the transmission coefficient, we investigate three main effects due to small perturbation: 1) a slow change of soliton parameters; 2) a deformation of its shape; 3) the formation of a soliton tail. We give in detail all the formulae which are necessary for further dealing with practical problems in nonlinear fiber optics (especially in femto-second region) and in nonlinear Alfven waves.
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