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: Burskii, V.P., Zhedanov, A.S.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2006
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
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
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.
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first_indexed 2025-12-07T18:04:07Z
last_indexed 2025-12-07T18:04:07Z
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