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Mat. Sb., 2005, Volume 196, Number 10, Pages 137–160 (Mi msb1429)  

This article is cited in 11 scientific papers (total in 11 papers)

Direct and inverse scattering problems for the perturbed Hill difference equation

Ag. Kh. Khanmamedov

Baku State University

Abstract: The direct and inverse scattering problems are studied for the perturbed Hill equation $(\widehat a_{n-1}+a_{n-1})y_{n-1} +( \widehat b_n+b_n)y_n+(\widehat a_n+a_n)y_{n+1}=\lambda y_n$, $n\in\Bbb Z$. The perturbation coefficients $a_n$$b_n$ are reconstructed from the periodic coefficients $\widehat a_n$, $\widehat b_n$ and the scattering data.

DOI: https://doi.org/10.4213/sm1429

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English version:
Sbornik: Mathematics, 2005, 196:10, 1529–1552

Bibliographic databases:

UDC: 517.9
MSC: Primary 39A05; Secondary 34L25, 34L40, 39A70
Received: 12.05.2004 and 04.10.2004

Citation: Ag. Kh. Khanmamedov, “Direct and inverse scattering problems for the perturbed Hill difference equation”, Mat. Sb., 196:10 (2005), 137–160; Sb. Math., 196:10 (2005), 1529–1552

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Kh. Khanmamedov, “The solution of Cauchy's problem for the Toda lattice with limit periodic initial data”, Sb. Math., 199:3 (2008), 449–458  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Ag. Kh. Khanmamedov, “Initial-boundary value problem for the Volterra lattice on a half-line with zero boundary condition”, Dokl. Math., 78:3 (2008), 848–850  mathnet  crossref  mathscinet  zmath  isi  elib
    3. Ag. Kh. Khanmamedov, “Inverse scattering problem for the difference Dirac operator on a half-line”, Dokl. Math., 79:1 (2009), 103–104  mathnet  crossref  mathscinet  zmath  isi  elib
    4. A. Kh. Khanmamedov, “The Cauchy problem for a semi-infinite Volterra chain with an asymptotically periodic initial condition”, Siberian Math. J., 51:2 (2010), 346–356  mathnet  crossref  mathscinet  isi  elib  elib
    5. A. Kh. Khanmamedov, “Inverse scattering problem for a discrete Sturm-Liouville operator on the entire line”, Doklady Mathematics, 81:2 (2010), 188–189  crossref  mathscinet  zmath  isi  elib
    6. A. Kh. Khanmamedov, “The inverse scattering problem for a discrete Sturm-Liouville equation on the line”, Sb. Math., 202:7 (2011), 1071–1083  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Khanmamedov A.Kh., Masmaliev G.M., “Spectral analysis of a class of Schrodinger difference operators”, Doklady Mathematics, 83:1 (2011), 111–112  crossref  mathscinet  zmath  zmath  isi  elib
    8. Iryna Egorova, Johanna Michor, Gerald Teschl, “Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data”, Math Phys Anal Geom, 2012  crossref  mathscinet  isi
    9. Khanmamedov A.Kh., Asadova L.K., “Integration of Toda Lattices with Steplike Initial Data”, Dokl. Math., 87:1 (2013), 36–38  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib
    10. M. G. Makhmudova, A. Kh. Khanmamedov, “Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice”, Comput. Math. Math. Phys., 55:12 (2015), 2008–2013  mathnet  crossref  crossref  mathscinet  isi  elib
    11. Manafov M.D. Kablan A. Bala B., “Parseval Equality of Discrete Sturm-Liouville Equation With Periodic Generalized Function Potentials”, AIP Conference Proceedings, 1991, ed. Sarikaya M. Akdemir A. Set E. Ekinci A., Amer Inst Physics, 2018, 020023  crossref  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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