  We consider the nonlinear scattering and transmission of an atom laser, or
Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The
nonlinearity inherent in this problem leads to several new physical features
beyond the well-known picture from single-particle quantum mechanics. We find
numerical evidence for a denumerably infinite string of bifurcations in the
transmission resonances as a function of nonlinearity and chemical potential,
when the potential barrier is wide compared to the wavelength of oscillations
in the condensate. Near the bifurcations, we observe extended regions of
near-perfect resonance, in which the barrier is effectively invisible to the
BEC. Unlike in the linear case, it is mainly the barrier width, not the height,
that controls the transmission behavior. We show that the potential barrier can
be used to create and localize a dark soliton or dark soliton train from a
phonon-like standing wave.
