Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
Analysis of PDEs
2008-04-24 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0604278,
title = {Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation},
author = {Vladimir P. Burskii and Alexei S. Zhedanov},
journal= {arXiv preprint arXiv:math/0604278},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/