  The truncated Wigner and positive-P phase-space representations are used to
study the dynamics of a one-dimensional Bose gas. This allows calculations of
the breathing quantum dynamics of higher-order solitons with 10^{3}-10^{5}
particles, as in realistic Bose-Einstein condensation (BEC) experiments.
Although classically stable, these decay quantum mechanically. Our calculations
show that there are large nonlocal correlations. These also violate the
Cauchy-Schwarz inequality, showing the presence of nonclassical quantum
entanglement.
