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Funktsional. Anal. i Prilozhen., 1975, Volume 9, Issue 1, Pages 65–66 (Mi faa2218)  

This article is cited in 18 scientific papers (total in 18 papers)

Brief communications

Inverse problem for periodic finite-zoned potentials in the theory of scattering

B. A. Dubrovin

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English version:
Functional Analysis and Its Applications, 1975, 9:1, 61–62

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Received: 04.04.1974

Citation: B. A. Dubrovin, “Inverse problem for periodic finite-zoned potentials in the theory of scattering”, Funktsional. Anal. i Prilozhen., 9:1 (1975), 65–66; Funct. Anal. Appl., 9:1 (1975), 61–62

Citation in format AMSBIB
\by B.~A.~Dubrovin
\paper Inverse problem for periodic finite-zoned potentials in the theory of scattering
\jour Funktsional. Anal. i Prilozhen.
\yr 1975
\vol 9
\issue 1
\pages 65--66
\jour Funct. Anal. Appl.
\yr 1975
\vol 9
\issue 1
\pages 61--62

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    This publication is cited in the following articles:
    1. A. R. Its, V. B. Matveev, “Schrödinger operators with finite-gap spectrum and $N$-soliton solutions of the Korteweg–de Vries equation”, Theoret. and Math. Phys., 23:1 (1975), 343–355  mathnet  crossref  mathscinet
    2. I. M. Krichever, “Potentials with zero coefficient of reflection on a background of finite-zone potentials”, Funct. Anal. Appl., 9:2 (1975), 161–163  mathnet  crossref  mathscinet  zmath
    3. B. A. Dubrovin, “Periodic problems for the Korteweg–de Vries equation in the class of finite band potentials”, Funct. Anal. Appl., 9:3 (1975), 215–223  mathnet  crossref  mathscinet  zmath
    4. B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Non-linear equations of Korteweg–de Vries type, finite-zone linear operators, and Abelian varieties”, Russian Math. Surveys, 31:1 (1976), 59–146  mathnet  crossref  mathscinet  zmath
    5. B. A. Dubrovin, “Konechnozonnye lineinye differentsialnye operatory i abelevy mnogoobraziya”, UMN, 31:4(190) (1976), 259–260  mathnet  mathscinet  zmath
    6. I. M. Krichever, “Methods of algebraic geometry in the theory of non-linear equations”, Russian Math. Surveys, 32:6 (1977), 185–213  mathnet  crossref  mathscinet  zmath
    7. I. M. Krichever, “Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model”, Funct. Anal. Appl., 20:3 (1986), 203–214  mathnet  crossref  mathscinet  zmath  isi
    8. P. G. Grinevich, “Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity”, Russian Math. Surveys, 55:6 (2000), 1015–1083  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. P. B. Djakov, B. S. Mityagin, “Instability zones of periodic 1-dimensional Schrödinger and Dirac operators”, Russian Math. Surveys, 61:4 (2006), 663–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Matveev, VB, “30 years of finite-gap integration theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 837  crossref  isi
    11. I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Russian Math. Surveys, 63:6 (2008), 1011–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. J. Harnad, V. Z. Enolski, “Schur function expansions of KP $\tau$-functions associated to algebraic curves”, Russian Math. Surveys, 66:4 (2011), 767–807  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Badanin A., Korotyaev E.L., “Even Order Periodic Operators on the Real Line”, Int Math Res Not, 2012, no. 5, 1143–1194  isi
    14. Andrei Ya. Maltsev, “Whitham's Method and Dubrovin–Novikov Bracket in Single-Phase and Multiphase Cases”, SIGMA, 8 (2012), 103, 54 pp.  mathnet  crossref
    15. Brezhnev Yu.V., “Spectral/Quadrature Duality: Picard-Vessiot Theory and Finite-Gap Potentials”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, eds. AcostaHumanez P., Finkel F., Kamran N., Olver P., Amer Mathematical Soc, 2012, 1–31  crossref  isi
    16. Badanin A., Korotyaev E., “Spectral Asymptotics for the Third Order Operator with Periodic Coefficients”, J. Differ. Equ., 253:11 (2012), 3113–3146  crossref  isi
    17. A. Badanin, E. Korotyaev, “Third order operator with periodic coefficients on the real axis”, St. Petersburg Math. J., 25:5 (2014), 713–734  mathnet  crossref  mathscinet  zmath  isi  elib
    18. Aleksandr O. Smirnov, Sergei G. Matveenko, Sergei K. Semenov, Elena G. Semenova, “Three-Phase Freak Waves”, SIGMA, 11 (2015), 032, 14 pp.  mathnet  crossref  mathscinet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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