Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition
The first order hyperbolic system of four equations on the semi-axis in the case of equal numbers of incident and scattered waves are considered when the velocities of the scattering waves are coincident. It is determined the criteria for inverse scattering problem (the problem of finding the potent...
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| Date: | 2023 |
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| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1014 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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oai:jmag.ilt.kharkiv.ua:article-10142024-10-11T14:48:59Z Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition Ismailov, Mansur I. обернена задача розсiювання загальнi крайовi умови гiперболiчна система першого порядку оператор перетворення Inverse scattering problem general boundary conditions first-order hyperbolic system transformation operator The first order hyperbolic system of four equations on the semi-axis in the case of equal numbers of incident and scattered waves are considered when the velocities of the scattering waves are coincident. It is determined the criteria for inverse scattering problem (the problem of finding the potential with respect to scattering operator) in terms of transmission matrices in two different boundary conditions. The uniqueness of the inverse scattering problem is studied by utilizing it to Gelfand-Levitan-Marchenko type linear integral equation. Mathematical Subject Classification 2020: 35R30, 35L50, 35P25, 37K15, 81U40 Розглянуто гiперболiчну систему чотирьох рiвнянь першого порядку на пiвосi у випадку рiвної кiлькостi падної i розсiяних хвиль за умови, що швидкостi розсiяних хвиль збiгаються. Установлено критерiї для оберненої задачi розсiювання (задачi знаходження потенцiалу за оператором розсiювання) в термiнах матриць передачi у двох рiзних крайових умовах. Вивчено єдинiсть оберненої задачi розсiювання за допомогою зведення задачi до лiнiйного iнтегрального рiвняння типу Ґельфанда–Левiтана–Марченка. Mathematical Subject Classification 2020: 35R30, 35L50, 35P25, 37K15, 81U40 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2023-07-31 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1014 10.15407/mag19.02.443 Journal of Mathematical Physics, Analysis, Geometry; Vol. 19 No. 2 (2023): Dedicated to Volodymyr Marchenko's 100th birthday; 443–455 Журнал математической физики, анализа, геометрии; Том 19 № 2 (2023): Присвячений 100-річчю від дня народження Володимира Олександровича Марченка; 443–455 Журнал математичної фізики, аналізу, геометрії; Том 19 № 2 (2023): Присвячений 100-річчю від дня народження Володимира Олександровича Марченка; 443–455 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1014/jm19-0443e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
|
| datestamp_date |
2024-10-11T14:48:59Z |
| collection |
OJS |
| language |
English |
| topic |
обернена задача розсiювання загальнi крайовi умови гiперболiчна система першого порядку оператор перетворення |
| spellingShingle |
обернена задача розсiювання загальнi крайовi умови гiперболiчна система першого порядку оператор перетворення Ismailov, Mansur I. Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| topic_facet |
обернена задача розсiювання загальнi крайовi умови гiперболiчна система першого порядку оператор перетворення Inverse scattering problem general boundary conditions first-order hyperbolic system transformation operator |
| format |
Article |
| author |
Ismailov, Mansur I. |
| author_facet |
Ismailov, Mansur I. |
| author_sort |
Ismailov, Mansur I. |
| title |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| title_short |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| title_full |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| title_fullStr |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| title_full_unstemmed |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition |
| title_sort |
inverse scattering problem for linear system of four-wave interaction problem on the half-line with a general boundary condition |
| title_alt |
Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary Condition Inverse Scattering Problem for Linear System of Four-Wave Interaction Problem on the Half-Line with a General Boundary |
| description |
The first order hyperbolic system of four equations on the semi-axis in the case of equal numbers of incident and scattered waves are considered when the velocities of the scattering waves are coincident. It is determined the criteria for inverse scattering problem (the problem of finding the potential with respect to scattering operator) in terms of transmission matrices in two different boundary conditions. The uniqueness of the inverse scattering problem is studied by utilizing it to Gelfand-Levitan-Marchenko type linear integral equation.
Mathematical Subject Classification 2020: 35R30, 35L50, 35P25, 37K15, 81U40 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2023 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1014 |
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AT ismailovmansuri inversescatteringproblemforlinearsystemoffourwaveinteractionproblemonthehalflinewithageneralboundarycondition AT ismailovmansuri inversescatteringproblemforlinearsystemoffourwaveinteractionproblemonthehalflinewithageneralboundary |
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2025-09-26T01:40:37Z |
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2025-09-26T01:40:37Z |
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1850836703302909952 |