Separation of variables via integral transformations

Details Separation of variables via integral transformations Separation of variables via integral transformations

1997-09-02

arxiv.org/abs/solv-int/9709001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 LaTex pages

Scientific paper

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 functional Bethe anzatz. The operators are shown to relate to separable variables. This approach is similar to the position-momentum transformation to action angle coordinates in the classical mechanics. General statements are illustrated by some examples.

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