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

Sylvester, John; Winebrenner, Dale; Gylys-Colwell, Fred

SIAM J. Appl. Math. 56, No. 3, 736-754 (1996).

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

Keywords:

trace formulas; layer stripping technique; inverse scattering problem; one-dimensional Helmholtz equation; nonlinear Plancherel equality; well-posedness