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Journal of Mathematical Physics, 1974
In a previous paper the inverse problem associated with a hyperbolic dispersive partial differential equation with smooth coefficients was considered. The inverse problem (the determination of the coefficients) was formulated in terms of a dual set of integral equations involving measurable quantities, the kernels of the transmission, and reflection ...
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In a previous paper the inverse problem associated with a hyperbolic dispersive partial differential equation with smooth coefficients was considered. The inverse problem (the determination of the coefficients) was formulated in terms of a dual set of integral equations involving measurable quantities, the kernels of the transmission, and reflection ...
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Inverse Scattering with Noisy Data
SIAM Journal on Scientific and Statistical Computing, 1986The accuracy of the peeling algorithm is analyzed for one-dimensional inverse problems in wave propagation. It is shown that in the case of noisy data it is possible to form an a posteriori estimate of the depth to which the results are valid. It is also shown that when additional information is known, that the impedance is piecewise constant, for ...
Bruckstein, A. M. +2 more
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A Multidimensional Inverse‐Scattering Method
Studies in Applied Mathematics, 1984A formal solution of the inverse scattering problem for the n‐dimensional; time‐dependent and time‐independent Schrödinger equations is given. Equations are found for reconstructing the potential from scattering data purely by quadratures. The solution also helps elucidate the problem of characterizing admissible scattering data.
Nachman, Adrian I., Ablowitz, Mark J.
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Inversion of Microwave Scattering Patterns
Canadian Journal of Physics, 1971An inversion method which reproduces the radial variation of dielectric constant in a dielectric target from its microwave scattering pattern is presented. Inversion criteria are developed showing what part of the target can be reconstructed. The technique is applied to experimentally measured scattering patterns.
Fedotowsky, A., Boivin, G., Tremblay, R.
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An approach to inverse scattering problems
Bioelectromagnetics, 1982AbstractThere are several reasons for investigating the inverse scattering problem in medical image processing. A typical case, that of ultrasonic fields, is considered. Assuming that a plane wave illuminates a weakly inhomogeneous two‐dimensional object, the fundamental equation is derived for the scattered waves in integral as well as in differential
M, Saito, T, Hayashi
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Inverse scattering for a plane screen
Applied Mathematics and Computation, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Inverse scattering in a layered medium
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999Summary: We present a uniqueness theorem in inverse scattering at a fixed energy for the wave equation in a layered medium. We acommodate the Faddeev theory of inverse scattering using the calculus of commutators.
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Lectures on the Inverse Scattering Transform
Studies in Applied Mathematics, 1978In 1967 a new method of mathematical physics was discovered by Gardner, Greene, Kruskal, and Miura. Their significant results have received much attention, and numerous developments have occurred within the decade. In this paper a survey of some of these developments is made. By and large the emphasis is on relating the key ideas via typical examples.
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Three-dimensional inverse scattering
1986We consider the problem of obtaining information about an inaccessible region of space from scattering experiments. Inverse scattering theory for the time-independent Schrodinger equation [Δ + h2−V(x)]φ(k,x) = 0 is summarized. It is most easily understood by considering the associated hyperbolic equation [Δ −aaa − V(x)]u(t,x) = 0.
Margaret Cheney +2 more
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Solitons and the Inverse Scattering Transform
1997This article is concerned with recent developments of the KdV equation and solitons, conservation laws, the Miura and the Gardner transformations continuous (or Lie) group for the KdV equation, similarity and rational solutions of the KdV equation, the inverse scattering transform (IST) method, Bäcklund transformations and a nonlinear superposition ...
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