Nonlinear Scattering of BECs on a Finite Barrier

We consider the scattering of a Bose-Einstein condensate (BEC) on a finite barrier. The nonlinear Schr\"{o}dinger equation (NLS) models the mean field of a BEC. The nonlinearity gives rise to several interesting physical and mathematical features which are not present in the linear problem. We present density and transmission plots for several physical cases, along with a discussion of these novel features. We also use the theory to model recent experiments.