Geodesic
Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell–Abel Equation
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Vladimir P. Burskii and Alexei S. Zhedanov},
     title = {Dirichlet and {Neumann} {Problems} for {String} {Equation,} {Poncelet} {Problem} and {Pell{\textendash}Abel} {Equation}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a40/}
}
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Vladimir P. Burskii; Alexei S. Zhedanov. Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell–Abel Equation. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a40/

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