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

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

2006-04-12

arxiv.org/abs/math/0604278v1

SIGMA 2 (2006), 041, 5 pages

Mathematics

Analysis of PDEs

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.041

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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