  The reflectionless transmission resonances in above-barrier reflection of
Bose-Einstein condensates by the Rosen-Morse potential are considered using the
mean field Gross-Pitaevskii approach. Applying an exact third order nonlinear
differential equation obeyed by the condensate's density, the exact solution of
the problem for the first resonance is derived. It is shown that in the
nonlinear case the total transmission is possible for positive potential
heights, i.e., for potential barriers. Further, it is shown that an appropriate
approximation for higher-order resonances can be constructed using a limit
solution of the equation for the density written as a root of a polynomial
equation of the third degree. Using this limit function and the solution for
the first resonance, a simple approximation for the shift of the nonlinear
resonance potential's depth from the corresponding linear resonance's position
is constructed for higher order resonances. The result is written as a linear
function of the resonance order. This behavior notably differs from the case of
the rectangular barrier for which the nonlinear shift is approximately constant
for all the resonance orders.
