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Funktsional. Anal. i Prilozhen., 1977, Volume 11, Issue 1, Pages 15–31 (Mi faa2041)  

This article is cited in 98 scientific papers (total in 98 papers)

Integration of nonlinear equations by the methods of algebraic geometry

I. M. Krichever

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English version:
Functional Analysis and Its Applications, 1977, 11:1, 12–26

Bibliographic databases:

UDC: 513.015.7+517.944
Received: 20.08.1976

Citation: I. M. Krichever, “Integration of nonlinear equations by the methods of algebraic geometry”, Funktsional. Anal. i Prilozhen., 11:1 (1977), 15–31; Funct. Anal. Appl., 11:1 (1977), 12–26

Citation in format AMSBIB
\by I.~M.~Krichever
\paper Integration of nonlinear equations by the methods of algebraic geometry
\jour Funktsional. Anal. i Prilozhen.
\yr 1977
\vol 11
\issue 1
\pages 15--31
\jour Funct. Anal. Appl.
\yr 1977
\vol 11
\issue 1
\pages 12--26

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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. Gel'fand, L. A. Dikii, “The resolvent and Hamiltonian systems”, Funct. Anal. Appl., 11:2 (1977), 93–105  mathnet  crossref  mathscinet  zmath
    3. B. A. Dubrovin, “Completely integrable Hamiltonian systems associated with matrix operators and Abelian varieties”, Funct. Anal. Appl., 11:4 (1977), 265–277  mathnet  crossref  mathscinet  zmath
    4. I. M. Krichever, “Algebraic curves and non-linear difference equations”, Russian Math. Surveys, 33:4 (1978), 255–256  mathnet  crossref  mathscinet  zmath
    5. I. M. Krichever, “Commutative rings of ordinary linear differential operators”, Funct. Anal. Appl., 12:3 (1978), 175–185  mathnet  crossref  mathscinet  zmath
    6. I. V. Cherednik, “Differential equations for the Baker–Akhiezer functions of algebraic curves”, Funct. Anal. Appl., 12:3 (1978), 195–203  mathnet  crossref  mathscinet  zmath
    7. I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286  mathnet  crossref  mathscinet  zmath
    8. Yu. I. Manin, “Matrix solitons and bundles over curves with singularities”, Funct. Anal. Appl., 12:4 (1978), 286–295  mathnet  crossref  mathscinet  zmath
    9. I. V. Cherednik, “Conservation laws and elements of scattering theory for principal chiral fields ($d=1$)”, Theoret. and Math. Phys., 41:2 (1979), 997–1002  mathnet  crossref  mathscinet  isi
    10. A. P. Veselov, “Hamiltonian formalism for the Novikov–Krichever equations for the commutativity of two operators”, Funct. Anal. Appl., 13:1 (1979), 1–6  mathnet  crossref  mathscinet  zmath
    11. I. V. Cherednik, “One generalization of the KdV and sin-Gordon differential equations”, Funct. Anal. Appl., 13:1 (1979), 68–69  mathnet  crossref  mathscinet  zmath
    12. 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
    13. G. B. Shabat, “A system of equations of S. P. Novikov”, Funct. Anal. Appl., 14:2 (1980), 158–160  mathnet  crossref  mathscinet  zmath
    14. I. M. Krichever, “Elliptic solutions of the Kadomtsev–Petviashvili equation and integrable systems of particles”, Funct. Anal. Appl., 14:4 (1980), 282–290  mathnet  crossref  mathscinet  zmath  isi
    15. B. A. Dubrovin, “Theta functions and non-linear equations”, Russian Math. Surveys, 36:2 (1981), 11–92  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. V. P. Maslov, G. A. Omel'yanov, “Asymptotic soliton-form solutions of equations with small dispersion”, Russian Math. Surveys, 36:3 (1981), 73–149  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. B. A. Dubrovin, “The Kadomtsev–Petviashvili equation and the relations between the periods of holomorphic differentials on Riemann surfaces”, Math. USSR-Izv., 19:2 (1982), 285–296  mathnet  crossref  mathscinet  zmath
    18. I. M. Krichever, “Baxter's equations and algebraic geometry”, Funct. Anal. Appl., 15:2 (1981), 92–103  mathnet  crossref  mathscinet  zmath  isi
    19. I. V. Cherednik, “Solutions of algebraic type of asymmetric differential equations”, Funct. Anal. Appl., 15:3 (1981), 231–232  mathnet  crossref  mathscinet  zmath  isi
    20. I. M. Krichever, “The Peierls model”, Funct. Anal. Appl., 16:4 (1982), 248–263  mathnet  crossref  mathscinet  isi
    21. I. V. Cherednik, “On the group-theoretical interpretation of Baker functions and $\tau$-functions”, Russian Math. Surveys, 38:6 (1983), 113–114  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    22. I. M. Gel'fand, I. V. Cherednik, “The abstract Hamiltonian formalism for the classical Yang–Baxter bundles”, Russian Math. Surveys, 38:3 (1983), 1–22  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. I. V. Cherednik, “Integrable differential equations and coverings of elliptic curves”, Math. USSR-Izv., 22:2 (1984), 357–377  mathnet  crossref  mathscinet  zmath
    24. I. M. Krichever, “The laplace method, algebraic curves, and nonlinear equations”, Funct. Anal. Appl., 18:3 (1984), 210–223  mathnet  crossref  mathscinet  zmath  isi
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    27. 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
    28. R. A. Sharipov, “Multiplet solutions of the Kadomtsev–Petviashvili equation against a finite-zone background”, Russian Math. Surveys, 42:5 (1987), 177–178  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213  mathnet  crossref  mathscinet  zmath  isi
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    34. 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
    35. A. V. Zabrodin, “Fermions on a Riemann surface and the Kadomtsev–Petviashvili equation”, Theoret. and Math. Phys., 78:2 (1989), 167–177  mathnet  crossref  mathscinet  zmath  isi
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    37. V. M. Buchstaber, I. M. Krichever, “Vector addition theorems and Baker–Akhiezer functions”, Theoret. and Math. Phys., 94:2 (1993), 142–149  mathnet  crossref  mathscinet  zmath  isi
    38. A. V. Marshakov, “On integrable systems and supersymmetric gauge theories”, Theoret. and Math. Phys., 112:1 (1997), 791–826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    39. I. M. Krichever, “Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations”, Funct. Anal. Appl., 31:1 (1997), 25–39  mathnet  crossref  crossref  mathscinet  zmath  isi
    40. 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
    41. A. D. Mironov, “Group theory approach to the $\tau$-function and its quantization”, Theoret. and Math. Phys., 114:2 (1998), 127–183  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    42. A. V. Marshakov, “Strings, SUSY gauge theories, and integrable systems”, Theoret. and Math. Phys., 121:2 (1999), 1409–1461  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    43. D. P. Novikov, “Algebraic-geometric solutions of the Krichever–Novikov equation”, Theoret. and Math. Phys., 121:3 (1999), 1567–1573  mathnet  crossref  crossref  mathscinet  zmath  isi
    44. Krichever, I, “Periodic and almost-periodic potentials in inverse problems”, Inverse Problems, 15:6 (1999), R117  isi
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    46. Treibich, A, “Difference analogs of elliptic KdV solitons and Schrodinger operators”, International Mathematics Research Notices, 2003, no. 6, 313  isi
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    50. 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
    51. V. M. Buchstaber, D. V. Leikin, “Addition Laws on Jacobian Varieties of Plane Algebraic Curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120  mathnet  mathscinet  zmath
    52. A. E. Mironov, “Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2”, Funct. Anal. Appl., 39:3 (2005), 240–243  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    53. S. V. Oblezin, “Isomonodromic deformations of $\mathfrak{sl}(2)$ Fuchsian systems on the Riemann sphere”, Mosc. Math. J., 5:2 (2005), 415–441  mathnet  mathscinet  zmath
    54. V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    55. Fledrich, P, “Hyperelliptic osculating covers and KdV solutions periodic in tau”, International Mathematics Research Notices, 2006, 73476  isi
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    58. E. Yu. Bunkova, V. M. Buchstaber, “Heat Equations and Families of Two-Dimensional Sigma Functions”, Proc. Steklov Inst. Math., 266 (2009), 1–28  mathnet  crossref  mathscinet  zmath  isi  elib
    59. Pavel Etingof, Eric Rains, “On Algebraically Integrable Differential Operators on an Elliptic Curve”, SIGMA, 7 (2011), 062, 19 pp.  mathnet  crossref  mathscinet
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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