Exponentially improved asymptotic expansions for resonances of an elliptic cylinder

Journal of Physics A: Mathematical and General

Volumn 33, Issue 16, 2000, Pages 3179-3208

  Ancey, S ^a   Folacci, A ^a   Gabrielli, P ^a  

^a Faculte des Sciences   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034724482     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/16/310     Document Type: Article

References (32)

1. Morse P M and Feshbach H 1953 Methods of Theoretical Physics vols 1, 2 (New York: McGraw-Hill)
2. Abramowitz M and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)
3. Erdelyi A 1953 Higher Transcendental Functions vol 3 (New York: McGraw-Hill)
4. Uslenghi P L E and Zitron N R 1987 The elliptic cylinder Electromagnetic and Acoustic Scattering by Simple Shapes ed J J Bowman, T B A Senior and P L E Uslenghi (New York: Hemisphere) pp 129-80
5. Keller J B 1956 Diffraction by a convex cylinder IRE Trans. 4 312-21
6. Keller J B 1958 A geometrical theory of diffraction Calculus of Variations and its Applications ed L M Graves (New York: McGraw-Hill) pp 27-52
7. Keller J B and Levy B R 1959 Diffraction by a smooth object Commun. Pure Appl. Math. 12 159-209
8. Keller J B 1962 Geometrical theory of diffraction J. Opt. Soc. Am. 52 116-30
9. Levy B R 1960 Diffraction by an elliptic cylinder J. Math. Mec. 9 147-65
10. Smilansky U 1995 Semiclassical quantisation of chaotic billiards - a scattering approach Mesoscopic Quantum Physics (Les Houches 1994, NATO ASI) ed E Ackermans, G Montambaux, J-L Pichard and J Zinn-Justin (Amsterdam: North-Holland) pp 373-433
11. Hamermesh M 1962 Group Theory and its Application to Physical Problems (New York: Dover)
12. Moser P J 1982 The isolation, identification and interpretation of resonances in the radar scattering cross section for conducting bodies of finite general shape PhD Thesis Department of Physics, The Catholic University of America, Washington, DC
13. Moser P J and Überall H 1983 Complex eigenfrequencies of axisymmetric, perfectly conducting bodies: radar spectroscopy Proc. IEEE 71 171-2
14. Bohigas O, Boosé D, Egydio de Carvalho R and Marvulle V 1993 Quantum tunneling and chaotic dynamics Nucl. Phys. A 560 197-210
15. Ayant Y and Arvieu R 1987 Semiclassical study of particle motion in two-dimensional and three-dimensional elliptic boxes: I J. Phys. A: Math. Gen. 30 4563
16. Waalkens H, Wiersig J and Dullin H R 1997 Elliptic quantum billiard Ann. Phys. 260 50
17. Sieber M 1997 Semiclassical transition from an elliptic to an oval billiard J. Phys. A: Math. Gen. 30 4563
18. Watson G N 1918 The diffraction of electric waves by the earth Proc. R. Soc. A 95 83-99
19. Sommerfeld A 1949 Partial Differential Equations in Physics (New York: Academic)
20. Levy B R and Keller J B 1960 Diffraction by a spheroid Can. J. Phys. 38 128-44
21. Hansen E B 1962 Scalar diffraction by an infinite strip and a circular disc J. Math. Phys. 41 229-45
22. Dingle R D 1973 Asymptotic Expansions: their Derivation and Interpretation (London: Academic)
23. Segur H, Tanveer S and Levine H (ed) 1991 Asymptotics Beyond all Orders (New York: Plenum)
24. Berry M V and Howls C J 1990 Hyperasymptotics Proc. R. Soc. A 430 653-68
25. Olver F W J 1954 The asymptotic solutions of linear differential equations of the second order for large values of a parameter Phil. Trans. R. Soc. A 247 307-27
26. Franz W 1957 Theorie der Beugung Elektromagnetischer Wellen (Berlin: Springer)
27. Streifer W and Kodis R D 1964 On the solution of a transcendental equation arising in the theory of scattering by a dielectric cylinder Q. Appl. Math. 21 285-98
28. Olver F W J 1954 The asymptotic expansion of Bessel functions of large order Phil. Trans. R. Soc. A 247 328-68
29. Fock V A 1965 Electromagnetic Diffraction and Propagation Problems (Oxford: Pergamon)
30. Bouche D. Molinet F and Mittra R 1996 Asymptotic Methods in Electromagnetics (Berlin: Springer)
31. Pathak P H 1979 An asymptotic analysis of the scattering of plane waves by a smooth convex cylinder Radio Sci. 14 419-35
32. Wolfram S 1996 The Mathematica Book (Cambridge: Cambridge University Press)