  Three-body collisions of ultracold identical Bose atoms under tight
cylindrical confinement are analyzed. A Feshbach resonance in two-body
collisions is described by a two-channel zero-range interaction. Elimination of
the closed channel in the three-body problem reduces the interaction to a
one-channel zero-range one with an energy dependent strength. The related
problem with an energy independent strength (the Lieb-Liniger-McGuire model)
has an exact solution and forbids all chemical processes, such as three-atom
association and diatom dissociation, as well as reflection in atom-diatom
collisions. The resonant case is analyzed by a numerical solution of the
Faddeev-Lovelace equations. The results demonstrate that as the internal
symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and
chemical reactions become allowed and may be observed in experiments.
