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 | 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.


References [Enhancements On Off] (What's this?)

  • [1] D. S. Moseley, Non-separable solutions of the Helmholtz wave equation, Quart. Appl. Math. 22, 354-357 (1965) MR 0183970
  • [2] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, New York, 1953, p. 755 MR 0059774


Additional Information

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

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