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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2006 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2006
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| Online Zugang: | 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 |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146170 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation |
| spellingShingle |
Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation Burskii, V.P. Zhedanov, A.S. |
| title_short |
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_sort |
dirichlet and neumann problems for string equation, poncelet problem and pell-abel equation |
| author |
Burskii, V.P. Zhedanov, A.S. |
| author_facet |
Burskii, V.P. Zhedanov, A.S. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146170 |
| 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. |
| work_keys_str_mv |
AT burskiivp dirichletandneumannproblemsforstringequationponceletproblemandpellabelequation AT zhedanovas dirichletandneumannproblemsforstringequationponceletproblemandpellabelequation |
| first_indexed |
2025-12-07T18:04:07Z |
| last_indexed |
2025-12-07T18:04:07Z |
| _version_ |
1850873634255536128 |