Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations Научная публикация
Журнал |
Mathematics
, E-ISSN: 2227-7390 |
||||||
---|---|---|---|---|---|---|---|
Вых. Данные | Год: 2023, Том: 11, Номер: 21, Номер статьи : 4458, Страниц : 31 DOI: 10.3390/math11214458 | ||||||
Ключевые слова | Gelfand–Levitan–Krein–Marchenko equation; inverse coefficient problem; inverse scattering problem | ||||||
Авторы |
|
||||||
Организации |
|
Информация о финансировании (1)
1 |
Министерство науки и высшего образования РФ Математический центр в Академгородке |
075-15-2019-1613, 075-15-2022-281 |
Реферат:
In this paper, we consider the Gelfand–Levitan–Marchenko–Krein approach. It is used for solving a variety of inverse problems, like inverse scattering or inverse problems for wave-type equations in both spectral and dynamic formulations. The approach is based on a reduction of the problem to the set of integral equations. While it is used in a wide range of applications, one of the most famous parts of the approach is given via the inverse scattering method, which utilizes solving the inverse problem for integrating the nonlinear Schrodinger equation. In this work, we present a short historical review that reflects the development of the approach, provide the variations of the method for 1D and 2D problems and consider some aspects of numerical solutions of the corresponding integral equations.
Библиографическая ссылка:
Kabanikhin S.I.
, Shishlenin M.A.
, Novikov N.S.
, Prokhoshin N.
Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations
Mathematics. 2023. V.11. N21. 4458 :1-31. DOI: 10.3390/math11214458 WOS Scopus РИНЦ OpenAlex
Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations
Mathematics. 2023. V.11. N21. 4458 :1-31. DOI: 10.3390/math11214458 WOS Scopus РИНЦ OpenAlex
Даты:
Поступила в редакцию: | 25 июн. 2023 г. |
Принята к публикации: | 16 окт. 2023 г. |
Опубликована в печати: | 27 окт. 2023 г. |
Опубликована online: | 27 окт. 2023 г. |
Идентификаторы БД:
Web of science: | WOS:001100201200001 |
Scopus: | 2-s2.0-85176336017 |
РИНЦ: | 63906171 |
OpenAlex: | W4387971124 |