  Generation of dark solitons from large initial excitations and their
evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a
harmonic potential is studied analytically and numerically. In the case of a
single deep soliton main characteristics of its motion such as a frequency and
amplitude of oscillations are calculated by means of the perturbation theory
which in the leading order results in a Newtonian dynamics, corrections to
which are computed as well. It is shown that long-time dynamics of a dark
soliton in a generic situation deviates substantially from outcomes of the
naive application of the Ehrenfest theorem. We also consider three different
techniques of controllable creation of multi-soliton structures (soliton
trains) from large initial excitations and calculate their initial parameters
(depths and velocities) with the use of a generalized Bohr-Sommerfeld
quantization rule. Multi-soliton effects are discussed.
