Barrier transmission for the nonlinear Schrödinger equation: surprises of nonlinear transport

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Abstract
In this paper we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schrödinger 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 wavefunction which will be of interest, e.g., for studies of coherent transport of Bose–Einstein condensates through mesoscopic waveguides.