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 experiments. Although classically stable, these decay quantum mechanically. Our calculations show that there are large nonlocal correlations and nonclassical quantum entanglement.
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