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The asymptotic analysis of canonical problems in high-frequency scattering theory: II. The circular and parabolic cylinders

  • W. G. C. Boyd (a1)

This is the second part of a two-part paper in which a systematic method is advanced for treating separation of variables problems asymptotically as the frequency becomes large. The method assumes an integral representation in which the contour of integration is the real axis. The contour is then deformed in the neighbourhood of the real axis to derive rigorous asymptotic expansions of the field. In this paper the method is applied to scattering in homogeneous media by the circular and parabolic cylinders.

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(6) D. S. Jones The theory of electromagnetism (Pergamon; Oxford, 1964).

(7) J. B. Keller Diffraction by a convex cylinder. I.R.E. Trans. Antennas Propag. 4 (1956), 312321.

(9) D. Ludwig Diffraction by a circular cavity. J. Mathematical Phys. 11 (1970), 16171630.

(10) H. M. Nussenzveig High-frequency scattering by an impenetrable sphere. Ann. Physics 34 (1965), 2395.

(11) H. M. Nussenlveig High-frequency scattering by a transparent sphere. I. Direct reflection and transmission. J. Mathematical Phys. 10 (1969), 82124.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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