Barrier transmission for the Nonlinear Schr\"odinger Equation: Surprises of nonlinear transport

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schroedinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave function which will be of interest, e.g., for studies of coherent transport of Bose-Einstein condensates through mesoscopic waveguide