Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2006
• ISSN: 1815-0659
• Hauptverfasser: Burskii, V.P., Zhedanov, A.S.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2006
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/146170
• 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.

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...