On the derivation of boundary integral equations for scattering by an infinite two-dimensional rough surface

Journal of Mathematical Physics

Volumn 39, Issue 2, 1998, Pages 894-912

  DeSanto, J A ^a   Martin, P A ^b  

^a Department of Metallurgical and Materials Engineering   (United States)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032338028     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532359     Document Type: Article

References (19)

1. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1983).
2. J. A. DeSanto and P. A. Martin, "On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface," J. Acoust. Soc. Am. 102, 67-77 (1997).
3. Sec. I A of Ref. 2.
4. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, 1944), 2nd ed.
5. P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Fields (Pergamon, Oxford, 1966).
6. J. A. DeSanto and P. A. Martin, "On angular-spectrum representations for scattering by infinite rough surfaces," Wave Motion 24, 421-433 (1996).
7. N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals (Dover, New York, 1986).
8. Sec. 8.4 of Ref. 7.
9. Eqs. 42, 44, and 46 in Sec. 8.4 of Ref. 7.
10. Eq. (8.4.46) of Ref. 7.
11. Sec. 9.6 of Ref. 7.
12. See Exercise 9.15(b) in Ref. 7.
13. A. Hulme, "The wave forces acting on a floating hemisphere undergoing forced periodic oscillations," J. Fluid Mech. 121, 443-463 (1982).
14. Sec. 5.2 of Ref. 4.
15. Eq. 2 on p. 379 of Ref. 4, with ν=1/2 and ψ=1/2π.
16. See p. 406 of Ref. 4.
17. See Sec. 8.2 of Ref. 7 for details.
18. G. C. Sherman, J. J. Stamnes, and É. Lalor, "Asymptotic approximations to angular-spectrum representations," J. Math. Phys. 17, 760-776 (1976).
19. See Ref. 2 for a discussion and references.