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arXiv:math/0604278 [math.AP]AbstractReferencesReviewsResources

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

Vladimir P. Burskii, Alexei S. Zhedanov

Published 2006-04-12Version 1

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.

Comments: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Journal: SIGMA 2 (2006), 041, 5 pages
Categories: math.AP, math-ph, math.MP
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