  A nonlinear Schroedinger model in a square well and managed nonlinearity is
shown to possess nonlinear states as continuous extensions of the linear
levels. The solutions are remarkably stable up to a threshold amplitude where a
soliton is emitted and propagates outside the well. The analytic expression of
the threshold is given in terms of the well size for each level. This process
of nonlinear tunneling results from an instability of the evanescent wave
inside the walls and can find experimental realization in a proposed nonlinear
fiber Bragg gratings resonator.
