Geodesic
Inverse scattering for the Bethe--Peierls model
Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 1, pp. 52-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the phased and phaseless inverse scattering problems for the Bethe–Peierls model. We give complete solutions of these problems including questions of uniqueness, nonuniqueness, reconstruction and characterization.
Keywords: inverse scattering, Schrödinger equation, exactly solvable models. 
@article{EJMCA_2018_6_1_a4,
     author = {R. G. Novikov},
     title = {Inverse scattering for the {Bethe--Peierls} model},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {52--55},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2018_6_1_a4/}
}
TY  - JOUR
AU  - R. G. Novikov
TI  - Inverse scattering for the Bethe--Peierls model
JO  - Eurasian journal of mathematical and computer applications
PY  - 2018
SP  - 52
EP  - 55
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJMCA_2018_6_1_a4/
LA  - en
ID  - EJMCA_2018_6_1_a4
ER  - 
%0 Journal Article
%A R. G. Novikov
%T Inverse scattering for the Bethe--Peierls model
%J Eurasian journal of mathematical and computer applications
%D 2018
%P 52-55
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJMCA_2018_6_1_a4/
%G en
%F EJMCA_2018_6_1_a4
R. G. Novikov. Inverse scattering for the Bethe--Peierls model. Eurasian journal of mathematical and computer applications, Tome 6 (2018) no. 1, pp. 52-55. http://geodesic.mathdoc.fr/item/EJMCA_2018_6_1_a4/

[1] A.D. Agaltsov, R.G. Novikov, “Simplest examples of inverse scattering on the plane at fixed energy”, HAL Id: hal-01570494, 1 (2017), 1-15

[2] S. Albeverio, F. Gesztesy, R.Hoegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics, Springer, New-York, 1988

[3] N.P.Badalyan, V.A. Burov, S.A.Morozov, and O.D.Rumyantseva,, “Sattering by acoustic boundary scatterers with small wave sizes and their reconstruction”, Acoustical Physics, 55:1 (2009), 1-7

[4] H.Bethe and R.Peierls, “Quantum theory of the diplon”, Proc. Roy. Soc. London Ser. A, 148 (1935), 146-156

[5] V.A. Burov and S.A.Morozov, “Relationship between the amplitude and phase of a signal scattered by a point-line acoustic inhomogeneity”, Acoustical Physics, 47:6 (2001), 659-664

[6] K.V.Dmitriev, “Matrix Green’s functions and their application in analyzing scattering by density and sound velocity inhomogeneities”, Acoustical Physics, 61:6 (2015), 632-635

[7] P.G.Grinevich and R.G.Novikov, “Multipoint scatterers with bound states at zero energy”, Theoretical and Mathematical Physics, 193:2 (2017), 1675-1679