  One-dimensional Bose gases are a useful testing-ground for quantum dynamics
in many-body theory. They allow experimental tests of many-body theory
predictions in an exponentially complex quantum system. Here we calculate the
dynamics of a higher-order soliton in the mesoscopic case of $N=10^3-10^4$
particles, giving predictions for quantum soliton breather relaxation. These
quantum predictions use a truncated Wigner approximation, which is a $1/N$
expansion, in a regime where other exactly known predictions are recovered to
high accuracy. Such dynamical calculations are testable in forthcoming BEC
experiments.
