Inverse Scattering Problem for One-Dimensional Schrödinger Equation with Discontinuity Conditions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 332-359 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The direct and inverse scattering problems for the second order ordinary differential equation on the whole axis with discontinuity conditions at some point are considered.
@article{JMAG_2013_9_3_a3,
     author = {H. M. Huseynov and J. A. Osmanli},
     title = {Inverse {Scattering} {Problem} for {One-Dimensional} {Schr\"odinger} {Equation} with {Discontinuity} {Conditions}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {332--359},
     year = {2013},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a3/}
}
TY  - JOUR
AU  - H. M. Huseynov
AU  - J. A. Osmanli
TI  - Inverse Scattering Problem for One-Dimensional Schrödinger Equation with Discontinuity Conditions
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2013
SP  - 332
EP  - 359
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a3/
LA  - en
ID  - JMAG_2013_9_3_a3
ER  - 
%0 Journal Article
%A H. M. Huseynov
%A J. A. Osmanli
%T Inverse Scattering Problem for One-Dimensional Schrödinger Equation with Discontinuity Conditions
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2013
%P 332-359
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a3/
%G en
%F JMAG_2013_9_3_a3
H. M. Huseynov; J. A. Osmanli. Inverse Scattering Problem for One-Dimensional Schrödinger Equation with Discontinuity Conditions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 332-359. http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a3/

[1] L. D. Faddeev, “On the Connection of the $S$-matrix and the Potential for the One-Dimensional Schrödinger Operator”, Dokl. Akad. Nauk SSSR, 121:1 (1958), 63–66 (Russian) | MR | Zbl

[2] L. D. Faddeev, “Properties of the $S$-matrix of the One-Dimensional Schrödinger Equations”, Trudy Mat. Inst. Steklov, 73, 1964, 314–336 (Russian) | MR | Zbl

[3] Sturm–Liouville Operators and Applications, Birkhäuser OT, 22, Basel–Boston, 1986 | MR | MR | Zbl

[4] I. M. Guseinov, “On the Continuity of the Coefficient of Reflection of the Schrödinger One-Dimensional Equation”, Diff. Uravn., 21:11 (1985), 1993–1995 (Russian) | MR

[5] 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”, J. Math. Phys., Anal. Geom., 3:1 (2007), 47–60 | MR | Zbl

[6] E. I. Zubkova, F. S. Rofe-Beketov, “Inverse Scattering Problem on the Axis for the Schrödinger Operator with Triangular $2\times 2$ Matrix Potential. II: Addition of the Discrete Spectrum”, J. Math. Phys., Anal. Geom., 3:2 (2007), 176–195 | MR | Zbl

[7] E. I. Zubkova, F. S. Rofe-Beketov, “Necessary and Sufficient Conditions in Inverse Scattering Operator with Triangular $2\times 2$ Matrix Potential”, J. Math. Phys., Anal. Geom., 5:3 (2009), 296–309 | MR | Zbl

[8] F. S. Rofe-Beketov, E. I. Zubkova, “Inverse Scattering Problem on the Axis for the Triangular $2\times 2$ Matrix Potential with a Virtual Level”, Methods of Functional Analysis and Topology, 15:4 (2009), 301–321 | MR | Zbl

[9] O. H. Hald, “Discontinuous Inverse Eigenvalue Problems”, Comm. Pure and Appl. Math., 37 (1984), 539–577 | DOI | MR | Zbl

[10] D. G. Shepelsky, “The Inverse Problem of Reconstruction of the Medium's Condictivity in a Class of Discontinuous and Functions”, Adv. in Sov. Math., 19 (1994), 209–232 | MR | Zbl

[11] M. Kobayashi, “A Uniqueness Proof of Discontinuous Inverse Sturm–Liouville Problems with Symmetric Potentials”, Inverse Problems, 5:5 (1989), 767–781 | DOI | MR | Zbl

[12] G. Frelling, V. Yurko, “Inverse Spectral Problems for Singular Non-Selfadjoint Differential Operators with Discontinuonities in an Interior Point”, Inverse Problems, 18 (2002), 757–773 | DOI | MR

[13] I. M. Guseinov, R. T. Pashaev, “On an Inverse Problem for a Second-Order Differential Equation”, Russian Math. Surv., 57:3 (2002), 597–598 (Russian) | DOI | MR | Zbl