ZhETF, Vol. 136,
No. 4,
p. 684 (October 2009)
(English translation  JETP,
Vol. 109, No. 4,
p. 585,
October 2009
available online at www.springer.com
)
RESONANCE REFLECTION BY THE ONEDIMENSIONAL ROSENMORSE POTENTIAL WELL IN THE GROSSPITAEVSKII PROBLEM
Ishkhanyan H.A., Krainov V.P.
Received: May 13, 2009
PACS: 05.30.Jp, 03.75.Lm, 03.75.Hh, 03.65.Ge
We consider the quantum abovebarrier reflection of a particle by the onedimensional RosenMorse potential well, for the nonlinear Schrödinger equation (the GrossPitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is exactly equal to zero for the linear Schrödinger equation. Then the reflection is determined by only a small nonlinear term in the GrossPitaevskii equation. The simple analytic expression is obtained for the reflection coefficient produced only by the nonlinearity. The analytic condition is found for the common action of the potential well and the nonlinearity to produce the zero reflection coefficient. The reflection coefficient is also derived analytically in the vicinity of a resonance shifted by the nonlinearity.

