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Funktsional. Anal. i Prilozhen., 1974, Volume 8, Issue 3, Pages 54–66 (Mi faa2358)  

This article is cited in 124 scientific papers (total in 124 papers)

The periodic problem for the Korteweg–de Vries equation

S. P. Novikov


Full text: PDF file (1667 kB)

English version:
Functional Analysis and Its Applications, 1974, 8:3, 236–246

Bibliographic databases:

Received: 18.02.1974

Citation: S. P. Novikov, “The periodic problem for the Korteweg–de Vries equation”, Funktsional. Anal. i Prilozhen., 8:3 (1974), 54–66; Funct. Anal. Appl., 8:3 (1974), 236–246

Citation in format AMSBIB
\Bibitem{Nov74}
\by S.~P.~Novikov
\paper The periodic problem for the Korteweg--de Vries equation
\jour Funktsional. Anal. i Prilozhen.
\yr 1974
\vol 8
\issue 3
\pages 54--66
\mathnet{http://mi.mathnet.ru/faa2358}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=382878}
\zmath{https://zbmath.org/?q=an:0299.35017}
\transl
\jour Funct. Anal. Appl.
\yr 1974
\vol 8
\issue 3
\pages 236--246
\crossref{https://doi.org/10.1007/BF01075697}


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    This publication is cited in the following articles:
    1. V. A. Marchenko, “The periodic Korteweg–de Vries problem”, Math. USSR-Sb., 24:3 (1974), 319–344  mathnet  crossref  mathscinet  zmath
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    3. 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
    4. I. M. Gel'fand, L. A. Dikii, “Asymptotic benaviour of the resolvent of Sturm–Liouville equations and the algebra of the Korteweg–de Vries equations”, Russian Math. Surveys, 30:5 (1975), 77–113  mathnet  crossref  mathscinet  zmath
    5. B. A. Dubrovin, “Inverse problem for periodic finite-zoned potentials in the theory of scattering”, Funct. Anal. Appl., 9:1 (1975), 61–62  mathnet  crossref  mathscinet  zmath
    6. A. R. Its, V. B. Matveev, “vHill's operator with finitely many gaps”, Funct. Anal. Appl., 9:1 (1975), 65–66  mathnet  crossref  mathscinet  zmath
    7. 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
    8. 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
    9. E. I. Dinaburg, Ya. G. Sinai, “The one-dimensional Schrödinger equation with a quasiperiodic potential”, Funct. Anal. Appl., 9:4 (1975), 279–289  mathnet  crossref  mathscinet  zmath
    10. 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
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    43. M. V. Babich, A. I. Bobenko, V. B. Matveev, “Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves”, Math. USSR-Izv., 26:3 (1986), 479–496  mathnet  crossref  mathscinet  zmath
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    45. 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
    46. R. A. Sharipov, “Finite-zone analogues of $N$-multiplet solutions of the Korteweg–de Vries equation”, Russian Math. Surveys, 41:5 (1986), 165–166  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    47. O. I. Mokhov, “On the Hamiltonian property of an arbitrary evolution system on the set of stationary points of its integral”, Math. USSR-Izv., 31:3 (1988), 657–664  mathnet  crossref  mathscinet  zmath
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    50. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124  mathnet  crossref  mathscinet  zmath  adsnasa
    51. 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
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    55. S. P. Novikov, “Quantization of finite-gap potentials and nonlinear quasiclassical approximation in nonperturbative string theory”, Funct. Anal. Appl., 24:4 (1990), 296–306  mathnet  crossref  mathscinet  zmath  isi
    56. I. Yu. Cherdantsev, R. A. Sharipov, “Finite-gap solutions of the Bullough–Dodd–Zhiber–Shabat equation”, Theoret. and Math. Phys., 82:1 (1990), 108–11  mathnet  crossref  mathscinet  zmath  isi
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    60. A. P. Veselov, A. B. Shabat, “Dressing Chains and Spectral Theory of the Schrödinger Operator”, Funct. Anal. Appl., 27:2 (1993), 81–96  mathnet  crossref  mathscinet  zmath  isi
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    64. 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
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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