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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 041, 5 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.041 (Mi sigma69) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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

Vladimir P. Burskiia, Alexei S. Zhedanovb

a Institute of Applied Mathematics and Mechanics NASU, Donetsk, 83114 Ukraine
b Donetsk Institute for Physics and Technology NASU, Donetsk, 83114 Ukraine
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DOI: https://doi.org/10.3842/SIGMA.2006.041
Abstract: 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.
Keywords: Dirichlet problem; Neumann problem; string equation; Poncelet problem; Pell–Abel equation.
Received: November 23, 2005; in final form March 20, 2006; Published online April 12, 2006
Bibliographic databases:
Document Type: Article
MSC: 35L20; 14H70; 13B25
Language: English
Citation: Vladimir P. Burskii, Alexei S. Zhedanov, “Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell–Abel Equation”, SIGMA, 2 (2006), 041, 5 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
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