Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
نویسندگان
چکیده
منابع مشابه
Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell–Abel Equation
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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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2006
ISSN: 1815-0659
DOI: 10.3842/sigma.2006.041