@article{JMAG_2007_3_1_a3,
author = {E. I. Zubkova and F. S. Rofe-Beketov},
title = {Inverse scattering problem on the axis for the {Schr\"odinger} operator with triangular $2\times 2$ matrix potential. {I.~Main} theorem},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {47--60},
year = {2007},
volume = {3},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a3/}
}
TY - JOUR AU - E. I. Zubkova AU - F. S. Rofe-Beketov TI - Inverse scattering problem on the axis for the Schrödinger operator with triangular $2\times 2$ matrix potential. I. Main theorem JO - Žurnal matematičeskoj fiziki, analiza, geometrii PY - 2007 SP - 47 EP - 60 VL - 3 IS - 1 UR - http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a3/ LA - en ID - JMAG_2007_3_1_a3 ER -
%0 Journal Article %A E. I. Zubkova %A F. S. Rofe-Beketov %T Inverse scattering problem on the axis for the Schrödinger operator with triangular $2\times 2$ matrix potential. I. Main theorem %J Žurnal matematičeskoj fiziki, analiza, geometrii %D 2007 %P 47-60 %V 3 %N 1 %U http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a3/ %G en %F JMAG_2007_3_1_a3
E. I. Zubkova; F. S. Rofe-Beketov. Inverse scattering problem on the axis for the Schrödinger operator with triangular $2\times 2$ matrix potential. I. Main theorem. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (2007) no. 1, pp. 47-60. http://geodesic.mathdoc.fr/item/JMAG_2007_3_1_a3/
[1] Birkháuser, Basel, 1986 | MR | Zbl
[2] L. D. Faddeyev, “Inverse Scattering Problem in Quantum Theory”, Modern Probl. Math., 3, VINITI, Moscow, 1974, 93–180 (Russian)
[3] VSP, Zeist, 1987 | MR
[4] Gordon and Breach, New York–London, 1963 | Zbl | Zbl
[5] E. I. Bondarenko, F. S. Rofe-Beketov, “Inverse Scattering Problem on the Semi-Axis for a System with a Triangular Matrix Potential”, Mat. phys., anal., geom., 10 (2003), 412–424 (Russian) | MR | Zbl
[6] V. A. Blashchak, “An Analogue of Inverse Problem in Scattering Theory for a Nonselfadjoint Operator, I”, Diff. Eq., 4:8 (1968), 1519–1533 ; “II”:10, 1915–1924 (Russian) | MR | Zbl
[7] B. Ya. Levin, “Fourier and Laplace Type Transformations via Solutions of Second Order Differential Equations”, Dokl. Acad. Sci. USSR, 106:2 (1956), 187–190 (Russian) | MR | Zbl
[8] Ungar., New York, 1968 | MR | Zbl | Zbl
[9] V. E. Lyantse, “An Analogue for Inverse Problem of Scattering Theory for Nonselfadjoint Operator”, Mat. Sb., 72:4 (1967), 537–557 (Russian) | MR | Zbl
[10] L. Martinez Alonso, E. Olmedilla, “Trace Identities in the Inverse Scattering Transform Method Associated with Matrix Schrödinger Operator”, J. Math. Phys., 23:11 (1982), 2116 | DOI | MR | Zbl
[11] Telecommun. and Radio Eng., 56:8,9 (2001), 4–29
[12] F. D. Gakhov, Boundary Problems, Fizmatgiz, Moscow, 1958 (Russian)
[13] L. P. Nizhnik, Inverse Scattering Problem for Hyperbolic Equations, Naukova Dumka, Kyiv, 1991 (Russian) | Zbl
[14] K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, With A Foreword by R. G. Newton, Springer-Verlag, New York–Heidelberg–Berlin, 1977 | MR | Zbl