Inverse scattering—exact solution of the Gel’fand-Levitan equation

DOI10.1063/1.525059zbMath0471.35073OpenAlexW2050309568MaRDI QIDQ3924609

Jeffrey M. Cohen, Kay R. Pechenick

Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525059

zbMATH Keywords

electromagnetic wavesreflection coefficientinverse scattering theoryGel'fand-Levitan equationionospheric electron densitysimultaneous linear equations with complex coefficients

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Partial differential equations of mathematical physics and other areas of application (35Q99) Waves and radiation in optics and electromagnetic theory (78A40) Geophysics (86A99)

Related Items (6)

A numerical resolution of the Gelfand-Levitan equation ⋮ On the solutions of the Gel’fand–Levitan equation ⋮ Inverse scattering with coinciding-pole reflection coefficients ⋮ Eigenvalues and eigenfunctions associated with the Gel’fand–Levitan equation ⋮ Exact solutions to the valley problem in inverse scattering ⋮ A Kalman filter solution of the inverse scattering problem with a rational reflection coefficient

Cites Work

• On the determination of a differential equation from its spectral function
• Reflectionless Transmission through Dielectrics and Scattering Potentials
• The inverse scattering problem when the reflection coefficient is a rational function
• An Example of the Effect of Rescaling of the Reflection Coefficient on the Scattering Potential for the One-Dimensional Schrodinger Equation

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