Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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: 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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DOI: https://doi.org/10.1090/qam/255956
Article copyright: © Copyright 1970 American Mathematical Society


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