We extend the perturbation theory of the nonlinear Schrödinger equation to the case of the integrable vector nonlinear Schrödinger equation. By applying the perturbed inverse scattering transform, we derive a set of nonlinear coupled evolution equations for the adiabatic change of the parameters of a vector soliton, in the . presence of a generic perturbation. We show that the same equations may also be obtained by means of a Lagrangian variational approach.
