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$R$-Separation of Variables for the Four-Dimensional Flat Space Laplace and Hamilton-Jacobi Equations

E. G. Kalnins and Willard Miller, Jr.
Transactions of the American Mathematical Society
Vol. 244 (Oct., 1978), pp. 241-261
DOI: 10.2307/1997897
Stable URL: http://www.jstor.org/stable/1997897
Page Count: 21
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$R$-Separation of Variables for the Four-Dimensional Flat Space Laplace and Hamilton-Jacobi Equations
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Abstract

All $R$-separable orthogonal coordinate systems for the complex equations $\Sigma^4_{i=1} \partial_{ii}\Psi = 0$ and $\Sigma^4_{i=1}(\partial_i W)^2 = 0$ are classified and it is shown that these equations separate in exactly the same systems.

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