On the Riccati equations for the scattering matrices in two dimensions

Inverse Problems

Volumn 13, Issue 1, 1997, Pages 1-13

  Chen, Y ^a   Rokhlin, V ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002422474     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/13/1/001     Document Type: Article

References (25)

1. Eyges L 1972 The Classical Eletromagnetic Field (New York: Dover)
2. Chadan K and Sabatier P C 1977 Inverse problems in quantum scattering theory (Berlin: Springer)
3. Kaveh M and Soumekh M 1987 Computer-assisted diffraction tomography Image Recovery: Theory and Application ed H Stark (New York: Academic) pp 369-413
4. Gel'fand I M and Levitan B M 1951 On the determination of a differential equation by its spectral function Dokl. Akad. USSR 77 557-60
5. Marchenko V A 1955 Reconstruction of potential energy from the phase of scattered waves Dokl. Akad. USSR 104 695-8
6. Faddeyev L D 1961 The inverse problem in the quantum theory of scattering J. Math. Phys. 4 72-104
7. Deift P and Trubowitz E 1979 Inverse scattering on the line Commun. Pure Appl. Math. 32 121-251
8. Crutchfield W Y 1983 Class of exact inversion solutions to vibrating string problem Phys. Lett. 98A 233-6
9. Sylvester J and Uhlmann G 1986 A uniqueness theorem for an inverse boundary value problem in electrical prospection Commun. Pure Appl. Math. 17 91-112
10. Somersalo J, Cheney M, Isaacson D and Isaacson E L 1991 Layer stripping: A direct numerical method for impedance imaging Inverse Problems 7 899-926
11. Newton R G 1989 Inverse Schrödinger Scattering in Three Dimensions (Berlin: Springer)
12. Chen Y and Rokhlin V 1992 On the inverse scattering problem for the Helmholtz equation in one dimension Inverse Problems 8 356-91
13. Sylvester J 1992 A convergent layer stripping algorithm for the radially symmetric impedance tomography problem Commun. PDE 17 1955-94
14. Courant R and Hilbert D 1962 Methods of Mathematical Physics vol 2 (New York: Wiley-Interscience)
15. Ikebe T 1959 Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory Arch. Rat. Mech. Anal. 5 1-34
16. Bleistein N 1984 Mathematical Methods for Wave Phenomena (New York: Academic)
17. Colton D and Kress R 1992 Integral Equation Methods in Scattering Theory (Applied Mathematical Science 93) (Berlin: Springer)
18. Colton D and Kress R 1991 Inverse Acoustic and Electromagnetic Scattering Theory (New York: Wiley-Interscience)
19. Twersky V 1952 Multiple scattering of radiation by an arbitrary configuration of parallel cylinders J. Acoust. Soc. Am. 24 42-6
20. Twersky V 1962 Multiple scattering of waves and optical phenomena J. Opt. Soc. Am. 52 145-71
21. Burke J E, Censor D and Twersky V 1965 Exact inverse-separation series for multiple scatterers in two dimensions J. Acoust. Soc. Am. 37 5-13
22. Corones J P et al 1983 Direct and inverse scattering in time domain via invariant imbedding J. Acoust. Soc. Am. 74 1535-42
23. Corones J P et al 1992 Invariant Imbedding and Inverse Problems (Philadelphia, PA: SIAM)
24. Abramowitz M and Stegun I 1965 Handbook of Mathematical Functions (New York: Dover)
25. Chen Y and Rokhlin V 1995 On the Riccati equations for the scattering matrices in two dimensions Technical Report 1081 Yale University, Department of Computer Science.