dorsal/arxiv
View SchemaSeparation of variables via integral transformations
| Authors | Ya. V. Lisitsyn, A. V. Shapovalov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9709001 |
| URL | https://arxiv.org/abs/solv-int/9709001 |
Abstract
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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"abstract": "For a system of linear partial differential equations (LPDEs) we introduce an\noperator equation for auxiliary operators. These operators are used to\nconstruct a kernel of an integral transformation leading the LPDE to the\nseparation of variables (SoV). The auxiliary operators are found for various\ntypes of the SoV including conventional SoV in the scalar second order LPDE and\nthe SoV by the functional Bethe anzatz. The operators are shown to relate to\nseparable variables. This approach is similar to the position-momentum\ntransformation to action angle coordinates in the classical mechanics. General\nstatements are illustrated by some examples.",
"arxiv_id": "solv-int/9709001",
"authors": [
"Ya. V. Lisitsyn",
"A. V. Shapovalov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Separation of variables via integral transformations",
"url": "https://arxiv.org/abs/solv-int/9709001"
},
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