  Perturbed version of the complex Toda chain (CTC) has been employed to
describe adiabatic interactions within N-soliton train of the nonlinear
Schrodinger equation (NLS). Perturbations induced by weak quadratic and
periodic external potentials are studied by both analytical and numerical
means. It is found that the perturbed CTC adequately models the N-soliton train
dynamics for both types of potentials. As an application of the developed
theory we consider the dynamics of a train of matter - wave solitons confined
to a parabolic trap and optical lattice, as well as tilted periodic potentials.
In the last case we demonstrate that there exist critical values of the
strength of the linear potential for which one or more localized states can be
extracted from a soliton train. An analytical expression for these critical
strengths for expulsion is also derived.
