Separation of variables via integral transformations
solv-int
2008-02-03 v1 可精确求解与可积系统
摘要
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.
引用
@article{arxiv.solv-int/9709001,
title = {Separation of variables via integral transformations},
author = {Ya. V. Lisitsyn and A. V. Shapovalov},
journal= {arXiv preprint arXiv:solv-int/9709001},
year = {2008}
}
备注
14 LaTex pages