Further properties of the nonseparable solutions of the Helmholtz wave equation
Author:
Donald S. Moseley
Journal:
Quart. Appl. Math. 27 (1970), 451-459
DOI:
https://doi.org/10.1090/qam/255956
MathSciNet review:
255956
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Abstract | References | Additional Information
Abstract: Nonseparable solutions ${W^{\left ( n \right )}}$ of $\left ( {{\nabla ^2} + {k^2}} \right ){W^{\left ( n \right )}} = 0$ are linearly independent, but inter-related through a generative differential operator. The nonseparable of order $n = 0$ is the familiar separable solution. In two cartesian coordinates, a sum of zero and second order solutions can describe transverse motion of a membrane of unique boundary contour. In three coordinates the same sum can describe acoustic pressure in a uniquely shaped cavity with pressure-release walls.
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Article copyright:
© Copyright 1970
American Mathematical Society