  We study the flow of bright solitons through two asymmetric potential wells.
The scattering of a soliton by certain type of single potential wells, e.g.,
Gaussian or Rosen-Morse, is distinguished by a critical velocity above which
solitons can transmit almost completely and below which solitons can reflect
nearly perfectly. For two such wells in series with certain parameter
combinations, we find that there is an appreciable velocity range for which
solitons can propagate in one direction only. Our study shows that this
directional propagation or diode behavior is due to a combined effect of the
sharp transition in the transport coefficients at the critical velocity and a
slight reduction in the center-of-mass speed of the soliton while it travels
across a potential well.
