Scattering and inverse scattering in one-dimensional nonhomogeneous media. (English) Zbl 0760.35032

Summary: The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrödinger equation \(d^ 2\psi/dx^ 2+k^ 2\psi=k^ 2P(x)\psi+Q(x)\psi\) with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the scattering matrix are obtained; the inverse scattering problem of recovering the restoring force when the wave speed and the scattering data are known are also solved.


35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81U40 Inverse scattering problems in quantum theory
35R30 Inverse problems for PDEs
Full Text: DOI


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