Abstract:
Sufficient conditions which are close to necessary are given in terms of only the coefficient r(k)=b(k)/a(k) for the solvability of the inverse problem of scattering theory for the Sturm–Liouville operator on the entire line.
Bibliography: 4 titles.
Citation:
B. M. Levitan, “Sufficient conditions for the solvability of the inverse problem of scattering theory on the entire line”, Math. USSR-Sb., 36:3 (1980), 323–329
\Bibitem{Lev79}
\by B.~M.~Levitan
\paper Sufficient conditions for the solvability of the inverse problem of scattering theory on the entire line
\jour Math. USSR-Sb.
\yr 1980
\vol 36
\issue 3
\pages 323--329
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\crossref{https://doi.org/10.1070/SM1980v036n03ABEH001816}
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Linking options:
https://www.mathnet.ru/eng/sm2309
https://doi.org/10.1070/SM1980v036n03ABEH001816
https://www.mathnet.ru/eng/sm/v150/i3/p350
This publication is cited in the following 6 articles:
B. D. Koshanov, A. P. Soldatov, Springer Proceedings in Mathematics & Statistics, 423, Differential Equations, Mathematical Modeling and Computational Algorithms, 2023, 215
A. P. Soldatov, “To the Solution of the Inverse Problem of Scattering Theory on the Entire Line”, Diff Equat, 58:11 (2022), 1482
Zhura N.A., Soldatov A.P., “To the Solution of the Inverse Sturm-Liouville Problem on the Real Axis”, Dokl. Math., 88:3 (2013), 695–699
Hryniv R.O., Mykytyuk Ya.V., Perry P.A., “Inverse Scattering for Schrodinger Operators with Miura Potentials, II. Different Riccati Representatives”, Commun. Partial Differ. Equ., 36:9 (2011), 1587–1623
Frayer C., Hryniv R.O., Mykytyuk Ya.V., Perry P.A., “Inverse Scattering for Schrodinger Operators with Miura Potentials: I. Unique Riccati Representatives and ZS-AKNS Systems”, Inverse Probl., 25:11 (2009), 115007
North-Holland Mathematics Studies, 167, Topics in Soliton Theory, 1991, 397
Citation in format AMSBIB
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