Separation of Variables for
نویسندگان
چکیده
منابع مشابه
Separation of variables for the Ruijsenaars system
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax matrix. Two different normalisations of the BA functions are analysed. The canonicity of the separated variab...
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The review is based on the author’s papers since 1985 in which a new approach to the separation of variables (SoV) has being developed. It is argued that SoV, understood generally enough, could be the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer...
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We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-toone mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the F...
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For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of variables (SoV). The auxiliary operators are found for various types of the SoV including conventional SoV in the scalar second order LPDE and the SoV by the fun...
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This talk consists of a proof of part of Stenger’s SINC-PACK computer package (an approx. 400-page tutorial + about 250 Matlab programs) that one can always achieve separation of variables when solving linear elliptic, parabolic, and hyperbolic PDE (partial differential equations) via use of Sinc methods. Some examples illustrating computer solutions via SINC-PACK will nevertheless be given in ...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2005
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2005-054-8