Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has pe...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2006
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146170 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation / V.P. Burskii, A.S. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716358081380352 |
|---|---|
| author | Burskii, V.P. Zhedanov, A.S. |
| author_facet | Burskii, V.P. Zhedanov, A.S. |
| citation_txt | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation / V.P. Burskii, A.S. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding Pell-Abel equation has a solution.
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| first_indexed | 2025-12-07T18:04:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146170 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:04:07Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Burskii, V.P. Zhedanov, A.S. 2019-02-07T20:05:57Z 2019-02-07T20:05:57Z 2006 Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation / V.P. Burskii, A.S. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 14 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35L20; 14H70; 13B25 https://nasplib.isofts.kiev.ua/handle/123456789/146170 We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding Pell-Abel equation has a solution. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation Article published earlier |
| spellingShingle | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation Burskii, V.P. Zhedanov, A.S. |
| title | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| title_full | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| title_fullStr | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| title_full_unstemmed | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| title_short | Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| title_sort | dirichlet and neumann problems for string equation, poncelet problem and pell-abel equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146170 |
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