Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems
Author:
Vaughan H. Weston
Journal:
Quart. Appl. Math. 15 (1958), 420-427
MSC:
Primary 35.00
DOI:
https://doi.org/10.1090/qam/98238
MathSciNet review:
98238
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Abstract: In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.
- Luther Pfahler Eisenhart, Separable systems of Stackel, Ann. of Math. (2) 35 (1934), no. 2, 284–305. MR 1503163, DOI https://doi.org/10.2307/1968433
- Parry Moon and Domina Eberle Spencer, Separability in a class of coordinate systems, J. Franklin Inst. 254 (1952), 227–242. MR 49438, DOI https://doi.org/10.1016/0016-0032%2852%2990460-2
V. Weston, Solutions of the toroidal wave equation and their applications, Ph.D. thesis, Univ. of Toronto. 1956
L. Eisenhart, Separable systems of Stäckel, Ann. Math. 35, 284 (1934)
P. Moon and D. E. Spencer, Separability in a class of coordinate systems, Franklin Inst. J. 254, 227 (1952)
V. Weston, Solutions of the toroidal wave equation and their applications, Ph.D. thesis, Univ. of Toronto. 1956
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Article copyright:
© Copyright 1958
American Mathematical Society
