  We present a simple approach for finding $N$-soliton solution and the
corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger
equation with nonvanishing boundary conditions. Soliton perturbation theory
based on the inverse scattering transform method is developed. As an
application of the present theory we consider the action of the diffusive-type
perturbation on a single bright/dark soliton.
