Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Multi-mode surface wave diffraction by a right-angled wedge


Authors: R. C. Morgan, S. N. Karp and Jr. Karal
Journal: Quart. Appl. Math. 24 (1966), 263-266
DOI: https://doi.org/10.1090/qam/99917
MathSciNet review: QAM99917
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Abstract | References | Additional Information

Abstract: This paper extends the phenomenological theory of multi-mode surface wave diffraction to a right-angled wedge configuration. The solution to a two-mode problem is obtained under the edge condition

$\displaystyle \sum\limits_{j = 0}^2 {\left\vert {\frac{{{\partial ^j}u}}{{\part... ...\right\vert = 0\left( {{r^{ - \left[ {1 + h} \right]}}} \right),0 \le h < 2/3} $

as $ r \to 0$. It is conjectured that the same procedure may be used to construct the solution to the corresponding $ N$-mode problem under the edge condition

$\displaystyle \sum\limits_{j = 0}^N {\left\vert {\frac{{{\partial ^j}u}}{{\part... ...r^{ - \left[ {\left( {2N - 1} \right)/3 + h} \right]}}} \right),0 \le h \le 2/3$

as $ r \to 0$.

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

  • [1] F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Excitation, Propagation and Diffraction, I. Plane Structures, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM-198, 1964
  • [2] F. C. Karal, and S. N. Karp, Phenomenological Theory of Multi-Mode Surface Wave Structures, Quasi-Optics Symposium, Brooklyn Polytechnic Inst., (John Wiley and Sons, New York, 1964). Also, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM-201, 1964
  • [3] F. C. Karal Jr., S. N. Karp, Ta-Shing Chu, and R. G. Kouyoumjian, Scattering of a surface wave by a discontinuity in the surface reactance on a right angled wedge, Comm. Pure Appl. Math. 14 (1961), 35–48. MR 0119790, https://doi.org/10.1002/cpa.3160140103
  • [4] Richard C. Morgan and Samuel N. Karp, Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory, Comm. Pure Appl. Math. 16 (1963), 45–56. MR 0149079, https://doi.org/10.1002/cpa.3160160107
  • [5] W. Magnus, and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, 2nd Ed.; Berlin, Springer, 1948
  • [6] R. C. Morgan, Uniqueness Theorem for a Multi-Mode Surface Wave Problem in Electromagnetic Diffraction Theory, New York Univ., Courant Inst. Math. Sci., Div. of Electromagnetic Res., Res. Rep. No. EM-212, 1965


Additional Information

DOI: https://doi.org/10.1090/qam/99917
Article copyright: © Copyright 1966 American Mathematical Society

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