Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-02-17 DOI:10.3842/SIGMA.2022.041

L. Bi, H. Cohl, H. Volkmer

引用次数: 2

Abstract

We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of ''flat rings''. These internal and external flat-ring harmonic functions are expressed in terms of simply-periodic Lamé functions. In a limiting case we obtain the expansion of the fundamental solution in toroidal coordinates.

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拉普拉斯方程的一个基本解在平环坐标系中的展开式

我们导出了拉普拉斯方程在三维欧氏空间的平环坐标系中的基本解的展开式。这个扩展是“平面环”内部和外部和谐的功能的双系列产品。这些内部和外部平环调和函数用简单的周期Lamé函数表示。在极限情况下，我们得到了基本解在环面坐标系中的展开式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.