Scattering by a potential using hyperbolic methods
Authors:
Alvin Bayliss, Yan Yan Li and Cathleen Synge Morawetz
Journal:
Math. Comp. 52 (1989), 321338
MSC:
Primary 65M99; Secondary 65N99, 81F99
MathSciNet review:
958869
Fulltext PDF Free Access
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Abstract: This is a preliminary note on a numerical timedependent approach to the inverse scattering problem where the data given is back scattering. The results in one space variable are both computed and are quite comparable to the best existing results. A corresponding algorithm is developed for two variables. A major stage is the computation of the forward problem for the wave equation with potential and with an incoming plane wave. Interesting developments are a boundary layer next to the propagating delta function and effective resolution of the scattered wave. It is assumed there are no bound states.
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 K. B. Bube & R. Burridge, "The onedimensional inverse problem of reflection seismology," SIAM Rev., v. 25, 1983, pp. 497559. MR 788323 (87c:86005)
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 R. Burridge, "The Gel'fandLevitan, the Marchenko, and the GopinathSondhi integral equations of inverse scattering theory, regarded in the context of inverse impulseresponse problems," Wave Motion, v. 2, 1980, pp. 305323. MR 593133 (82d:81144)
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 D. C. Stickler, "Inverse scattering in a stratified medium," J. Acoust. Soc. Amer., v. 74, 1983, pp. 9941005. MR 717863 (84k:76098)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909588691
PII:
S 00255718(1989)09588691
Keywords:
Scattering from a potential,
inverse problems
Article copyright:
© Copyright 1989 American Mathematical Society
