منابع مشابه
Fixed-energy inverse scattering
The author’s method for solving inverse scattering problem with fixed-energy data is described. Its comparison with the method based on the D-N map is given. A new inversion procedure is formulated. c © 2008 Elsevier Ltd. All rights reserved. MSC: 35R30; 47H17; 65M30; 81U05 PACS: 03.80.+r.; 03.65.Nk
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1 Introduction In this lecture the author reviews his results on multidimensional inverse scattering. References to the works of other authors can be found in [20]. Five topics are briefly discussed:-1) property C with constraints and new type of the uniqueness theorems for inverse scattering,-2) inversion of noisy discrete fixed-energy 3D scattering data and error estimates,-3) variational pri...
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The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong in the sense that its foundations are wrong: in general it cannot be carried through because its basic integral equation may be not solvable for some r > 0 and in this case the method breaks down; ...
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Let A q (α ′ , α, k) be the scattering amplitude, corresponding to a local potential q(x), x ∈ R 3 , q(x) = 0 for |x| > a, where a > 0 is a fixed number, α ′ , α ∈ S 2 are unit vectors, S 2 is the unit sphere in R 3 , α is the direction of the incident wave, k 2 > 0 is the energy. We prove that given an arbitrary function f (α ′) ∈ L 2 (S 2), an arbitrary fixed α 0 ∈ S 2 , an arbitrary fixed k ...
متن کاملInverse Scattering at a Fixed Energy for Long - Range Potentials ∗ †
In this paper we consider the inverse scattering problem at a fixed energy for the Schrödinger equation with a long-range potential in R, d ≥ 3. We prove that the long-range part can be uniquely reconstructed from the leading forward singularity of the scattering amplitude at some positive energy.
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2008
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.02.041