  We analytically solve two problems that may be useful in the context of the
recent observation of matter wave bright solitons in a one-dimensional
attractive atomic Bose gas. The first problem is strictly beyond mean field:
  From the Bethe ansatz solution we extract the internal correlation function
of the particle positions in the quantum soliton, that is for a fixed center of
mass position. The second problem is solved in the limit of a large number of
particles, where the mean field theory is asymptotically correct: It deals with
the number of excitations created by the opening of the trap, starting from a
pure soliton in a weakly curved harmonic potential.
