  The stability properties and perturbation-induced dynamics of the full set of
stationary states of the nonlinear Schroedinger equation are investigated
numerically in two physical contexts: periodic solutions on a ring and
confinement by a harmonic potential. Our comprehensive studies emphasize
physical interpretations useful to experimentalists. Perturbation by stochastic
white noise, phase engineering, and higher order nonlinearity are considered.
We treat both attractive and repulsive nonlinearity and illustrate the
soliton-train nature of the stationary states.
