  The existence and stability of solitonic states in one-dimensional repulsive
Bose-Einstein condensates is investigated within a fully many-body framework by
considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of
stationary, shape-invariant states propagating at constant velocity are
explicitly found and compared to the known solution of the Gross-Pitaevskii
equation. The typical features attributed to nonlinearity are thus recovered in
a purely linear theory, provided the full many-particle physics is correctly
accounted for. However, the formation dynamics predicted by the
Gross-Pitaevskii approximation considerably differs from the exact many-body
evolution.
