%0 Journal Article
%T Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
%A Vladimir P. Burskii
%A Alexei S. Zhedanov
%J Mathematics
%D 2006
%I arXiv
%R 10.3842/SIGMA.2006.041
%X 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.
%U http://arxiv.org/abs/math/0604278v1