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Dokl. Akad. Nauk SSSR, 1976, Volume 229, Number 1, Pages 15–18 (Mi dan40452)  

This article is cited in 63 scientific papers (total in 64 papers)


The Schrödinger equation in a periodic field and Riemann surfaces

B. A. Dubrovin, I. M. Krichever, S. P. Novikov

Landau Institute for Theoretical Physics, USSR Academy of Sciences, Chernogolovka Moscow region

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UDC: 513.835
Received: 19.02.1976

Citation: B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “The Schrödinger equation in a periodic field and Riemann surfaces”, Dokl. Akad. Nauk SSSR, 229:1 (1976), 15–18

Citation in format AMSBIB
\by B.~A.~Dubrovin, I.~M.~Krichever, S.~P.~Novikov
\paper The Schr\"odinger equation in a periodic field and Riemann surfaces
\jour Dokl. Akad. Nauk SSSR
\yr 1976
\vol 229
\issue 1
\pages 15--18

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    This publication is cited in the following articles:
    1. 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
    2. I. M. Krichever, “Integration of nonlinear equations by the methods of algebraic geometry”, Funct. Anal. Appl., 11:1 (1977), 12–26  mathnet  crossref  mathscinet  zmath
    3. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over algebraic curves and non-linear equations”, Russian Math. Surveys, 35:6 (1980), 53–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. B. A. Dubrovin, “Theta functions and non-linear equations”, Russian Math. Surveys, 36:2 (1981), 11–92  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. P. G. Grinevich, R. G. Novikov, “Analogs of multisoliton potentials for the two-dimensional Schrödinger operator”, Funct. Anal. Appl., 19:4 (1985), 276–285  mathnet  crossref  mathscinet  zmath  isi
    6. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Russian Math. Surveys, 41:2 (1986), 1–49  mathnet  crossref  mathscinet  zmath  isi
    7. P. G. Grinevich, S. V. Manakov, “Inverse scattering problem for the two-dimensional Schrödinger operator, the $\bar\partial$-method and nonlinear equations”, Funct. Anal. Appl., 20:2 (1986), 94–103  mathnet  crossref  mathscinet  zmath
    8. I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, riemann surfaces and structures of the theory of solitons”, Funct. Anal. Appl., 21:2 (1987), 126–142  mathnet  crossref  mathscinet  zmath  isi
    9. R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. P. G. Grinevich, S. P. Novikov, “Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state”, Funct. Anal. Appl., 22:1 (1988), 19–27  mathnet  crossref  mathscinet  zmath  isi
    11. S. M. Natanzon, “Nonsingular finite-zone two-dimensional Schrödinger operators and prymians of real curves”, Funct. Anal. Appl., 22:1 (1988), 68–70  mathnet  crossref  mathscinet  zmath  isi
    12. R. G. Novikov, “Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$”, Funct. Anal. Appl., 22:4 (1988), 263–272  mathnet  crossref  mathscinet  zmath  isi
    13. S. M. Natanzon, “Prymians of real curves and their applications to the effectivization of Schrödinger operators”, Funct. Anal. Appl., 23:1 (1989), 33–45  mathnet  crossref  mathscinet  zmath  isi
    14. I. M. Krichever, “Spectral theory of two-dimensional periodic operators and its applications”, Russian Math. Surveys, 44:2 (1989), 145–225  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. I. A. Taimanov, “Two-dimensional finite-zone Schrodinger potential operators”, Funct. Anal. Appl., 24:1 (1990), 76–77  mathnet  crossref  mathscinet  zmath  isi
    16. I. A. Taimanov, “Prym varieties of branched coverings and nonlinear equations”, Math. USSR-Sb., 70:2 (1991), 367–384  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. S. M. Natanzon, “Differential equations on the Prym theta function. a realness criterion for two-dimensional, finite-zone, potential Schrödinger operators”, Funct. Anal. Appl., 26:1 (1992), 13–20  mathnet  crossref  mathscinet  zmath  isi
    18. I. M. Krichever, “Two-Dimensional Algebraic-Geometric Operators with Self-Consistent Potentials”, Funct. Anal. Appl., 28:1 (1994), 21–32  mathnet  crossref  mathscinet  zmath  isi
    19. V. M. Buchstaber, V. Z. Ènol'skii, “Abelian Bloch solutions of the two-dimensional Schrödinger equation”, Russian Math. Surveys, 50:1 (1995), 195–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. A. P. Veselov, S. P. Novikov, “Exactly soluble periodic two-dimensional Schrödinger operators”, Russian Math. Surveys, 50:6 (1995), 1316–1317  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    22. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    24. A. V. Zabrodin, “A survey of Hirota's difference equations”, Theoret. and Math. Phys., 113:2 (1997), 1347–1392  mathnet  crossref  crossref  mathscinet  isi
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    29. A. A. Oblomkov, “Difference Operators on Two-Dimensional Regular Lattices”, Theoret. and Math. Phys., 127:1 (2001), 435–445  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    45. D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Siberian Math. J., 52:3 (2011), 394–401  mathnet  crossref  mathscinet  isi
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