  We investigate the dynamics of a Bose--Einstein condensate (BEC) in a
triple-well trap in a three-level approximation. The inter-atomic interactions
are taken into account in a mean-field approximation (Gross-Pitaevskii
equation), leading to a nonlinear three-level model. New eigenstates emerge due
to the nonlinearity, depending on the system parameters. Adiabaticity breaks
down if such a nonlinear eigenstate disappears when the parameters are varied.
The dynamical implications of this loss of adiabaticity are analyzed for two
important special cases: A three level Landau-Zener model and the STIRAP
scheme. We discuss the emergence of looped levels for an equal-slope
Landau-Zener model. The Zener tunneling probability does not tend to zero in
the adiabatic limit and shows pronounced oscillations as a function of the
velocity of the parameter variation. Furthermore we generalize the STIRAP
scheme for adiabatic coherent population transfer between atomic states to the
nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds
the detuning.
