On a reflection coefficient for the Schrödinger operator with a smooth potential

TitleOn a reflection coefficient for the Schrödinger operator with a smooth potential
Publication TypeJournal Article
Year of Publication2014
AuthorsGladka, ZM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.09.007
Issue9
SectionMathematics
Pagination7-12
Date Published9/2014
LanguageRussian
Abstract

The decaying properties of the reflection coefficients are studied for the Schrödinger operator with a smooth steplike potential depending on the number of derivatives of the potential and its speed of tending to its background asymptotics.

Keywordsreflection coefficient, Schrödinger operator
References: 

1. Marchenko V. A. The inverse scattering problem and its applications to NLPDE. In: Scattering and Inverse Scattering in Pure and Applied Science (Ed. R. Pike, P. Sabatier), San Diego: Academic Press, 2002: 1695–1706. https://doi.org/10.1016/b978-012613760-6/50094-2
2. Egorova I., Grunert K., Teschl G. Nonlinearity, 2009, 22: 1431–1457. https://doi.org/10.1088/0951-7715/22/6/009
3. Cohen A., Kappeler T. Indiana Univ. Math. J., 1985, 34, No 1: 127–180. https://doi.org/10.1512/iumj.1985.34.34008
4. Bazargan J. Dopov. Nac. akad. nauk Ukr., 2008, No 4: 7–11 (in Russian).
5. Marchenko V. A. Sturm–Liouville operators and applications, Basel: Birkhauser, 1986. https://doi.org/10.1007/978-3-0348-5485-6
6. Buslaev V. S., Fomin V. N. Vestn. Leningr. un-ta, 1962, 17, No 1: 56–64 (in Russian).