ZhETF, Vol. 136,
p. 684 (October 2009)
(English translation - JETP,
Vol. 109, No. 4,
available online at www.springer.com
RESONANCE REFLECTION BY THE ONE-DIMENSIONAL ROSEN-MORSE POTENTIAL WELL IN THE GROSS-PITAEVSKII 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 above-barrier reflection of a particle by the one-dimensional Rosen-Morse potential well, for the nonlinear Schrödinger equation (the Gross-Pitaevskii 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 Gross-Pitaevskii 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.