Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

A parameter-expansion method for the scattering of plane waves by an elliptic cylindrical and a hyperboloidal scatterer


Author: Thomas M. Acho
Journal: Quart. Appl. Math. 57 (1999), 601-620
MSC: Primary 35P25; Secondary 35C20, 35J05, 78A45
DOI: https://doi.org/10.1090/qam/1724295
MathSciNet review: MR1724295
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The scattered wave components of a plane polarized electromagnetic wave by an elliptic cylindrical scatterer are obtained as a parameter expansion of the more exact circular cylindrical obstacle. The scattering potential of a scalar wave by a hyperboloidal scatterer as a parameter expansion of a circular cone is also obtained. The parameter of expansion in both cases is the semi-interfocal distance.


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

  • [1] M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965
  • [2] J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi (eds.), Electromagnetic and acoustic scattering by simple shapes, A Summa Book, Hemisphere Publishing Corp., New York, 1987. Revised reprint of the 1969 edition. MR 1111017
  • [3] S. K. Datta, Interaction of a plane compressional wave with a rigid spheroidal inclusion, Quart. Appl. Math. 31 (1973)
  • [4] Victor A. Erma, Perturbation approach to the electrostatic problem for irregularly shaped conductors, J. Mathematical Phys. 4 (1963), 1517–1526. MR 0168259, https://doi.org/10.1063/1.1703933
  • [5] Victor A. Erma, An exact solution for the scattering of electromagnetic waves from conductors of arbitrary shape. I. Case of cylindrical symmetry, Phys. Rev. (2) 173 (1968), 1243–1257. MR 0246572
  • [6] I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1963
  • [7] A. C. Hewson, An Introduction to the Theory of Electromagnetic Waves, Longman Group Ltd., London, 1970
  • [8] P. M. Morse and H. Feshback, Methods of Mathematical Physics, McGraw-Hill Book Co., New York, 1953
  • [9] A. Sommerfeld and J. Rung, Anvedung der Vektorrechung aud die Griendlages det gometrischen Optik, Ann. Physik. 35, 277-298 (1911)
  • [10] Thomas M. Acho, Scalar wave scattering of a prolate spheroid as a parameter expansion of that of a sphere, Quart. Appl. Math. 50 (1992), no. 3, 451–468. MR 1178427, https://doi.org/10.1090/qam/1178427

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35P25, 35C20, 35J05, 78A45

Retrieve articles in all journals with MSC: 35P25, 35C20, 35J05, 78A45


Additional Information

DOI: https://doi.org/10.1090/qam/1724295
Article copyright: © Copyright 1999 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website