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Layer stripping for the Helmholtz equation. (English) Zbl 0851.34011

Summary: We develop a new layer stripping technique for the inverse scattering problem for the one-dimensional Helmholtz equation on the half line. The technique eliminates the use of “trace formulas”, relying instead on a nonlinear Plancherel equality that provides a simple and precise characterization of the reflection data. We prove both convergence of the algorithm and well-posedness of the forward and inverse scattering problems.

MSC:

34A55 Inverse problems involving ordinary differential equations
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