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Inverse Scattering on the Half Line for the Matrix Schrödinger Equation

Inverse Scattering on the Half Line for the Matrix Schrödinger Equation

The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix potential is integrable, is selfadjoint, and has a finite first mom...

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Main Authors: Aktosun, Tuncay, Weder, Ricardo
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/145874
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spelling irk-123456789-1458742019-02-03T01:22:59Z Inverse Scattering on the Half Line for the Matrix Schrödinger Equation Aktosun, Tuncay Weder, Ricardo The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix potential is integrable, is selfadjoint, and has a finite first moment. The corresponding scattering data set is constructed, and such scattering data sets are characterized by providing a set of necessary and sufficient conditions assuring the existence and uniqueness of the one-toone correspondence between the scattering data set and the input data set containing the potential and boundary matrices. The work presented here provides a generalization of the classic result by Agranovich and Marchenko from the Dirichlet boundary condition to the general selfadjoint boundary condition. На пiвпрямiй розглянуто матричне рiвняння Шредiнгера iз загальною самоспряженою крайовою умовою в нулi, яка задається двома матрицями, що задовольняють певнi умови. Вважається, що матричний потенцiал є самоспряженим, iнтегровним та має скiнченний перший момент. Побудовано вiдповiдну множину даних розсiяння. Цю множину даних розсiювання характеризовано набором необхiдних i достатнiх умов, якi гарантують єдинiсть та взаємно однозначну вiдповiднiсть мiж множиною даних розсiяння та множиною вхiдних даних, яка мiстить потенцiал та крайовi матрицi. Ця робота надає узагальнення з крайової умови Дiрiхле на загальну самоспряжену крайову умову для класичного результату Аграновича та Марченка. 2018 Article Inverse Scattering on the Half Line for the Matrix Schrödinger Equation / Tuncay Aktosun, Ricardo Weder // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 3. — С. 237-269. — Бібліогр.: 24 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.03.237 Mathematics Subject Classification 2000: 34L25, 34L40, 81U05 http://dspace.nbuv.gov.ua/handle/123456789/145874 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix potential is integrable, is selfadjoint, and has a finite first moment. The corresponding scattering data set is constructed, and such scattering data sets are characterized by providing a set of necessary and sufficient conditions assuring the existence and uniqueness of the one-toone correspondence between the scattering data set and the input data set containing the potential and boundary matrices. The work presented here provides a generalization of the classic result by Agranovich and Marchenko from the Dirichlet boundary condition to the general selfadjoint boundary condition.
format Article
author Aktosun, Tuncay
Weder, Ricardo
spellingShingle Aktosun, Tuncay
Weder, Ricardo
Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
Журнал математической физики, анализа, геометрии
author_facet Aktosun, Tuncay
Weder, Ricardo
author_sort Aktosun, Tuncay
title Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
title_short Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
title_full Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
title_fullStr Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
title_full_unstemmed Inverse Scattering on the Half Line for the Matrix Schrödinger Equation
title_sort inverse scattering on the half line for the matrix schrödinger equation
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/145874
citation_txt Inverse Scattering on the Half Line for the Matrix Schrödinger Equation / Tuncay Aktosun, Ricardo Weder // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 3. — С. 237-269. — Бібліогр.: 24 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT aktosuntuncay inversescatteringonthehalflineforthematrixschrodingerequation
AT wederricardo inversescatteringonthehalflineforthematrixschrodingerequation
first_indexed 2023-05-20T17:23:17Z
last_indexed 2023-05-20T17:23:17Z
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