$N$-soliton solutions and perturbation theory for the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions

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.