Scattering by a potential using hyperbolic methods

Bayliss, Alvin; Li, Yan Yan; Morawetz, Cathleen Synge

doi:10.1090/S0025-5718-1989-0958869-1

Scattering by a potential using hyperbolic methods
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by Alvin Bayliss, Yan Yan Li and Cathleen Synge Morawetz PDF

Math. Comp. 52 (1989), 321-338 Request permission

Abstract:

This is a preliminary note on a numerical time-dependent 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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