Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Fundamental'nye Napravleniya"
General information
Latest issue

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.:

Personal entry:
Save password
Forgotten password?

Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 1985, Volume 4, Pages 179–277 (Mi intf37)  

This article is cited in 69 scientific papers (total in 69 papers)

Integrable systems. I

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

Full text: PDF file (11500 kB)

Bibliographic databases:
UDC: 512.77+517.912+517.958

Citation: B. A. Dubrovin, I. M. Krichever, S. P. Novikov, “Integrable systems. I”, Dynamical systems – 4, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 4, VINITI, Moscow, 1985, 179–277

Citation in format AMSBIB
\by B.~A.~Dubrovin, I.~M.~Krichever, S.~P.~Novikov
\paper Integrable systems.~I
\inbook Dynamical systems~--~4
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.
\yr 1985
\vol 4
\pages 179--277
\publ VINITI
\publaddr Moscow

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. A. A. Kirillov, D. V. Yur'ev, “Kähler geometry of the infinite-dimensional homogeneous manifold $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Funct. Anal. Appl., 20:4 (1986), 322–324  mathnet  crossref  mathscinet  zmath  isi
    2. A. P. Veselov, “Integration of the stationary problem for a classical spin chain”, Theoret. and Math. Phys., 71:1 (1987), 446–450  mathnet  crossref  mathscinet  isi
    3. E. D. Belokolos, V. Z. Ènol'skii, “Expression of parameters of solutions of algebraically integrable nonlinear equations in terms of theta constants”, Funct. Anal. Appl., 21:1 (1987), 60–62  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. A. A. Kirillov, D. V. Yur'ev, “Kähler geometry of the infinite-dimensional homogeneous space $M=\operatorname{Diff}_+(S^1)/\operatorname{Rot}(S^1)$”, Funct. Anal. Appl., 21:4 (1987), 284–294  mathnet  crossref  mathscinet  zmath  isi
    6. S. B. Kuksin, “Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation”, Math. USSR-Sb., 64:2 (1989), 397–413  mathnet  crossref  mathscinet  zmath
    7. A. P. Veselov, “Integrable discrete-time systems and difference operators”, Funct. Anal. Appl., 22:2 (1988), 83–93  mathnet  crossref  mathscinet  zmath  isi
    8. I. M. Krichever, “Method of averaging for two-dimensional “integrable” equations”, Funct. Anal. Appl., 22:3 (1988), 200–213  mathnet  crossref  mathscinet  zmath  isi
    9. A. G. Reiman, M. A. Semenov-Tian-Shansky, “Lax representation with a spectral parameter for the kowalevski top and its generalizations”, Funct. Anal. Appl., 22:2 (1988), 158–160  mathnet  crossref  mathscinet  isi
    10. I. D. Chueshov, “Structure of the equilibrium states of a class of dynamical systems associated with Lie–Poisson brackets”, Theoret. and Math. Phys., 75:3 (1988), 640–644  mathnet  crossref  mathscinet  zmath  isi
    11. 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
    12. 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
    13. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    15. O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. A. I. Bobenko, “Constant mean curvature surfaces and integrable equations”, Russian Math. Surveys, 46:4 (1991), 1–45  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. T. A. Ivanova, “Nahm's equations and autodual connections”, Russian Math. Surveys, 46:4 (1991), 174–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. B. S. Kruglikov, “Topological classification of Leggett systems in an integrable case for $^3\mathrm{He-A}$”, Russian Math. Surveys, 46:4 (1991), 179–181  mathnet  crossref  mathscinet  adsnasa  isi
    19. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. 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
    21. S. S. Safin, R. A. Sharipov, “Bäcklund autotransformation for the equation $u_{xt}=e^u-e^{-2u}$”, Theoret. and Math. Phys., 95:1 (1993), 462–470  mathnet  crossref  mathscinet  zmath
    22. A. V. Aminova, “Pseudo–Riemannian manifolds with common geodesies”, Russian Math. Surveys, 48:2 (1993), 105–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. Yu. N. Fedorov, “Lax representations with a spectral parameter defined on coverings of hyperelliptic curves”, Math. Notes, 54:1 (1993), 728–738  mathnet  crossref  mathscinet  zmath  isi
    24. V. Yu. Novokshenov, “Whitham Deformations of Top-Like Integrable Dynamical Systems”, Funct. Anal. Appl., 27:2 (1993), 118–127  mathnet  crossref  mathscinet  zmath  isi
    25. D. V. Yur'ev, “Quantum projective field theory: Quantum-field analogs of the Euler–Arnol'd equations in projective $G$ multiplets”, Theoret. and Math. Phys., 98:2 (1994), 147–161  mathnet  crossref  mathscinet  zmath  isi
    26. L. M. Lerman, Ya. L. Umanskii, “Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III. Realization”, Sb. Math., 186:10 (1995), 1477–1491  mathnet  crossref  mathscinet  zmath  isi
    27. A. V. Aminova, “Projective transformations and symmetries of differential equation”, Sb. Math., 186:12 (1995), 1711–1726  mathnet  crossref  mathscinet  zmath  isi
    28. V. L. Alekseev, “On non-local Hamiltonian operators of hydrodynamic type connected with Whitham's equations”, Russian Math. Surveys, 50:6 (1995), 1253–1255  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    29. 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
    30. 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
    31. D. P. Novikov, R. K. Romanovskii, “On a method for constructing algebro-geometric solutions to the zero curvature equation”, Theoret. and Math. Phys., 110:1 (1997), 47–56  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. 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
    33. 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
    34. 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
    35. R. K. Romanovskii, S. G. Sadovnichuk, “A direct method of construction of two-zone solutions of nonlinear equations”, Math. Notes, 66:3 (1999), 323–327  mathnet  crossref  crossref  mathscinet  zmath  isi
    36. I. M. Krichever, S. P. Novikov, “Holomorphic bundles and commuting difference operators. Two-point constructions”, Russian Math. Surveys, 55:3 (2000), 586–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    37. A. N. Tyurin, “On Bohr–Sommerfeld bases”, Izv. Math., 64:5 (2000), 1033–1064  mathnet  crossref  crossref  mathscinet  zmath  isi
    38. G. Falqui, F. Magri, G. Tondo, “Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy”, Theoret. and Math. Phys., 122:2 (2000), 176–192  mathnet  crossref  crossref  mathscinet  zmath  isi
    39. A. S. Gorsky, “Integrable many-body systems and gauge theories”, Theoret. and Math. Phys., 125:1 (2000), 1305–1348  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    40. A. L. Gorodentsev, A. N. Tyurin, “Abelian Lagrangian algebraic geometry”, Izv. Math., 65:3 (2001), 437–467  mathnet  crossref  crossref  mathscinet  zmath
    41. È. B. Vinberg, “Commutative homogeneous spaces and co-isotropic symplectic actions”, Russian Math. Surveys, 56:1 (2001), 1–60  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    42. M. Pedroni, “Bi-Hamiltonian Aspects of the Separability of the Neumann System”, Theoret. and Math. Phys., 133:3 (2002), 1722–1729  mathnet  crossref  crossref  mathscinet  zmath  isi
    43. M. A. Olshanetsky, “The large $N$ limits of integrable models”, Mosc. Math. J., 3:4 (2003), 1307–1331  mathnet  crossref  mathscinet  zmath
    44. I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    45. 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
    46. 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
    47. O. V. Efimovskaya, “Factorization of loop algebras over $\mathrm{so}(4)$ and integrable nonlinear differential equations”, J. Math. Sci., 144:2 (2007), 3926–3937  mathnet  crossref  mathscinet  zmath  elib
    48. A. V. Aminova, N. A.-M. Aminov, “Fourth-order differential systems with a four-dimensional solvable symmetry group that does not contain the abelian subgroup $G_3$”, Russian Math. (Iz. VUZ), 49:6 (2005), 10–24  mathnet  mathscinet  zmath
    49. A. V. Marshakov, “Matrix Model and Stationary Problem in the Toda Chain”, Theoret. and Math. Phys., 146:1 (2006), 1–12  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    50. R. I. Bogdanov, “Nonlocal integrals and conservation laws in the theory of nonlinear solitons”, Journal of Mathematical Sciences, 149:4 (2008), 1400–1416  mathnet  crossref  mathscinet
    51. 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
    52. A. V. Aminova, N. A. Aminov, “Projective geometry of systems of second-order differential equations”, Sb. Math., 197:7 (2006), 951–975  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    53. A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, “Integrable magnetic geodesic flows on Lie groups”, Theoret. and Math. Phys., 156:2 (2008), 1127–1141  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    54. 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
    55. A. V. Aminova, N. A.-M. Aminov, “The projective geometric theory of systems of second-order differential equations: straightening and symmetry theorems”, Sb. Math., 201:5 (2010), 631–643  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    56. A. V. Domrin, “Meromorphic extension of solutions of soliton equations”, Izv. Math., 74:3 (2010), 461–480  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    57. A. V. Badanin, E. L. Korotyaev, “Spectral estimates for a periodic fourth-order operator”, St. Petersburg Math. J., 22:5 (2011), 703–736  mathnet  crossref  mathscinet  zmath  isi
    58. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    59. Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.  mathnet  crossref  mathscinet
    60. A. V. Domrin, “On holomorphic solutions of equations of Korteweg–de Vries type”, Trans. Moscow Math. Soc., 73 (2012), 193–206  mathnet  crossref  mathscinet  zmath  elib
    61. L. D. Faddeev, “The new life of complete integrability”, Phys. Usp., 56:5 (2013), 465–472  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    62. A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    63. M. V. Shamolin, “Some classes of integrable problems in spatial dynamics of a rigid body in a nonconservative force field”, J. Math. Sci. (N. Y.), 210:3 (2015), 292–330  mathnet  crossref
    64. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    65. M. V. Shamolin, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590  mathnet  crossref
    66. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    67. Simonetta Abenda, Petr G. Grinevich, “Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case”, Proc. Steklov Inst. Math., 302 (2018), 1–15  mathnet  crossref  crossref  mathscinet  isi  elib
    68. V. Yu. Novokshenov, “Parametricheskii rezonans v integriruemykh sistemakh i usrednenie na rimanovykh poverkhnostyakh”, Differentsialnye uravneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 65–80  mathnet  mathscinet
    69. V. M. Buchstaber, A. V. Mikhailov, “Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves”, Russian Math. Surveys, 76:4 (2021), 587–652  mathnet  crossref  crossref  isi
  • Number of views:
    This page:3823
    Full text:1957

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021