Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential
A method for solving the integral Gelfand – Levitan – Marchenko (GLM) equation for the Sturm – Liouville operator with a step-type potential is obtained. The scattering function is found explicitly. An associated system of infinite recurrence equations is solved. The integral operator kernel is pre...
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| Дата: | 2003 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2003
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/176153 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential / V.P. Revenko // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 74-82. — Бібліогр.: 7 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-176153 |
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dspace |
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| spelling |
irk-123456789-1761532021-02-04T01:29:57Z Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential Revenko, V.P. A method for solving the integral Gelfand – Levitan – Marchenko (GLM) equation for the Sturm – Liouville operator with a step-type potential is obtained. The scattering function is found explicitly. An associated system of infinite recurrence equations is solved. The integral operator kernel is presented in an exact form using Bessel function. A series of new integral representations for Bessel functions is obtained for the first time. Запропоновано спосiб розв’язання iнтегрального рiвняння Гельфанда – Левiтана – Марченка для оператора Штурма – Лiувiлля у випадку ступiнчастого потенцiала, заданого на додатнiй пiвосi або на всiй дiйснiй осi. Розв’язано (точно) асоцiйовану з задачею нескiнченну систему лiнiйних рекурентних рiвнянь. Отримано ядра iнтегральних операторiв у явному виглядi через функцiї Бесселя. Знайдено вперше ряд нових iнтегральних спiввiдношень для функцiй Бесселя. 2003 Article Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential / V.P. Revenko // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 74-82. — Бібліогр.: 7 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/176153 517.986 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A method for solving the integral Gelfand – Levitan – Marchenko (GLM) equation for the Sturm – Liouville operator with a step-type potential is obtained. The scattering function is found explicitly. An associated
system of infinite recurrence equations is solved. The integral operator kernel is presented in an exact form
using Bessel function. A series of new integral representations for Bessel functions is obtained for the first
time. |
| format |
Article |
| author |
Revenko, V.P. |
| spellingShingle |
Revenko, V.P. Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential Нелінійні коливання |
| author_facet |
Revenko, V.P. |
| author_sort |
Revenko, V.P. |
| title |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential |
| title_short |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential |
| title_full |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential |
| title_fullStr |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential |
| title_full_unstemmed |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential |
| title_sort |
determination of an exact solution to the integral gelfand - levitan - marchenko equation for the sturm - liouville operators with the step-type potential |
| publisher |
Інститут математики НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/176153 |
| citation_txt |
Determination of an exact solution to the integral Gelfand - Levitan - Marchenko equation for the Sturm - Liouville operators with the step-type potential / V.P. Revenko // Нелінійні коливання. — 2003. — Т. 6, № 1. — С. 74-82. — Бібліогр.: 7 назв. — англ. |
| series |
Нелінійні коливання |
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AT revenkovp determinationofanexactsolutiontotheintegralgelfandlevitanmarchenkoequationforthesturmliouvilleoperatorswiththesteptypepotential |
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2025-07-15T13:48:21Z |
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2025-07-15T13:48:21Z |
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1837720982747348992 |