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

Vladimir P. Burskii·Alexei S. Zhedanov
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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.

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Vladimir P. Burskii, Alexei S. Zhedanov. 2006-04-12. Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation. https://doi.org/10.3842/sigma.2006.041

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