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
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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.
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S. K. Datta, Interaction of a plane compressional wave with a rigid spheroidal inclusion, Quart. Appl. Math. 31 (1973)
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A. C. Hewson, An Introduction to the Theory of Electromagnetic Waves, Longman Group Ltd., London, 1970
P. M. Morse and H. Feshback, Methods of Mathematical Physics, McGraw-Hill Book Co., New York, 1953
A. Sommerfeld and J. Rung, Anvedung der Vektorrechung aud die Griendlages det gometrischen Optik, Ann. Physik. 35, 277–298 (1911)
- 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, DOI https://doi.org/10.1090/qam/1178427
M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965
J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, North-Holland Publishing Company, Amsterdam, 1969
S. K. Datta, Interaction of a plane compressional wave with a rigid spheroidal inclusion, Quart. Appl. Math. 31 (1973)
V. A. Erma, Perturbation approach to the electrostatic problem for irregularly shaped conductors, Journal of Mathematical Physics 4, No. 2, 1517–1526 (1963)
V. A. Erma, An exact solution for the scattering of electromagnetic waves from conductors of arbitrary shape, 1. Case of cylindrical symmetry, Physical Review 173, 1243–1257 (1968)
I. S. Gradshteyn and I. W. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1963
A. C. Hewson, An Introduction to the Theory of Electromagnetic Waves, Longman Group Ltd., London, 1970
P. M. Morse and H. Feshback, Methods of Mathematical Physics, McGraw-Hill Book Co., New York, 1953
A. Sommerfeld and J. Rung, Anvedung der Vektorrechung aud die Griendlages det gometrischen Optik, Ann. Physik. 35, 277–298 (1911)
Thomas M. Acho, Scalar wave scattering of a prolate spheroid as a parameter expansion of that of a sphere, Quart. Appl. Math. 50, 451–468 (1992)
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Article copyright:
© Copyright 1999
American Mathematical Society
