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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 1983, Volume 23, Pages 79–136 (Mi intd69)  

This article is cited in 17 scientific papers (total in 17 papers)

Nonlinear equations and elliptic curves

I. M. Krichever


Abstract: The main ideas of global finite-zone integration are presented, and a detailed analysis is given of applications of the technique developed to some problems based on the theory of elliptic functions. In the work the Peierls model is integrated as an important application of the algebrogeometric spectral theory of difference operators.

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English version:
Journal of Soviet Mathematics, 1985, 28:1, 51–90

Bibliographic databases:

UDC: 517.957+512.7

Citation: I. M. Krichever, “Nonlinear equations and elliptic curves”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 23, VINITI, Moscow, 1983, 79–136; J. Soviet Math., 28:1 (1985), 51–90

Citation in format AMSBIB
\Bibitem{Kri83}
\by I.~M.~Krichever
\paper Nonlinear equations and elliptic curves
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1983
\vol 23
\pages 79--136
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd69}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=734314}
\zmath{https://zbmath.org/?q=an:0595.35087}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 1
\pages 51--90
\crossref{https://doi.org/10.1007/BF02104896}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. M. Krichever, “The laplace method, algebraic curves, and nonlinear equations”, Funct. Anal. Appl., 18:3 (1984), 210–223  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655  mathnet  crossref  mathscinet  zmath
    4. 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
    5. I. M. Krichever, S. P. Novikov, “Algebras of virasoro type, energy-momentum tensor, and decomposition operators on Riemann surfaces”, Funct. Anal. Appl., 23:1 (1989), 19–33  mathnet  crossref  mathscinet  zmath  isi
    6. A. O. Smirnov, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, Theoret. and Math. Phys., 78:1 (1989), 6–13  mathnet  crossref  mathscinet  isi
    7. V. P. Kotlyarov, “Asymptotic solitons of the sine-Gordon equation”, Theoret. and Math. Phys., 80:1 (1989), 679–689  mathnet  crossref  mathscinet  isi
    8. I. M. Krichever, A. V. Zabrodin, “Spin generalization of the Ruijsenaars–Schneider model, the non-Abelian Toda chain, and representations of the Sklyanin algebra”, Russian Math. Surveys, 50:6 (1995), 1101–1150  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. O. K. Sheinman, “Weil Modules with Highest Weight for Affine Lie Algebras on Riemann Surfaces”, Funct. Anal. Appl., 29:1 (1995), 44–55  mathnet  crossref  mathscinet  zmath  isi
    10. A. V. Zabrodin, “A survey of Hirota's difference equations”, Theoret. and Math. Phys., 113:2 (1997), 1347–1392  mathnet  crossref  crossref  mathscinet  isi
    11. A. V. Penskoi, “Canonically conjugate variables for the Volterra lattice with periodic boundary conditions”, Math. Notes, 64:1 (1998), 98–109  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. D. V. Talalaev, “The Elliptic Gaudin System with Spin”, Theoret. and Math. Phys., 130:3 (2002), 361–374  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. D. V. Talalaev, A. V. Chervov, “Hitchin System on Singular Curves”, Theoret. and Math. Phys., 140:2 (2004), 1043–1072  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. A. E. Mironov, “Ierarkhiya uravnenii Veselova–Novikova i integriruemye deformatsii minimalnykh lagranzhevykh torov v $\mathbb CP^2$”, Sib. elektron. matem. izv., 1 (2004), 38–46  mathnet  mathscinet  zmath
    15. A. V. Domrin, “The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker–Akhiezer Function”, Theoret. and Math. Phys., 144:3 (2005), 1264–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. A. V. Domrin, “Remarks on the Local Version of the Inverse Scattering Method”, Proc. Steklov Inst. Math., 253 (2006), 37–50  mathnet  crossref  mathscinet
    17. I. M. Krichever, “Commuting Difference Operators and the Combinatorial Gale Transform”, Funct. Anal. Appl., 49:3 (2015), 175–188  mathnet  crossref  crossref  isi  elib
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