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Funktsional. Anal. i Prilozhen., 1977, Volume 11, Issue 2, Pages 11–27 (Mi faa2064)  

This article is cited in 28 scientific papers (total in 29 papers)

The resolvent and Hamiltonian systems

I. M. Gel'fand, L. A. Dikii


Full text: PDF file (1815 kB)
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English version:
Functional Analysis and Its Applications, 1977, 11:2, 93–105

Bibliographic databases:

UDC: 517.4+519.3
Received: 22.12.1976

Citation: I. M. Gel'fand, L. A. Dikii, “The resolvent and Hamiltonian systems”, Funktsional. Anal. i Prilozhen., 11:2 (1977), 11–27; Funct. Anal. Appl., 11:2 (1977), 93–105

Citation in format AMSBIB
\Bibitem{GelDik77}
\by I.~M.~Gel'fand, L.~A.~Dikii
\paper The resolvent and Hamiltonian systems
\jour Funktsional. Anal. i Prilozhen.
\yr 1977
\vol 11
\issue 2
\pages 11--27
\mathnet{http://mi.mathnet.ru/faa2064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=442984}
\zmath{https://zbmath.org/?q=an:0357.58005|0412.58018}
\transl
\jour Funct. Anal. Appl.
\yr 1977
\vol 11
\issue 2
\pages 93--105
\crossref{https://doi.org/10.1007/BF01081887}


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    Citing articles on Google Scholar: Russian citations, English citations
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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 calculus of jets and nonlinear Hamiltonian systems”, Funct. Anal. Appl., 12:2 (1978), 81–94  mathnet  crossref  mathscinet  zmath
    3. 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
    4. D. R. Lebedev, Yu. I. Manin, “Gel'fand–Dikii Hamiltonian operator and the coadjoint representation of the volterra group”, Funct. Anal. Appl., 13:4 (1979), 268–273  mathnet  crossref  mathscinet  zmath
    5. F. A. Berezin, A. M. Perelomov, “Group theoretic interpretation of equations of Korteweg - de Vries type”, Funct. Anal. Appl., 14:2 (1980), 119–121  mathnet  crossref  mathscinet  zmath
    6. A. G. Reiman, M. A. Semenov-Tian-Shansky, “A family of Hamiltonian structures, hierarchy of Hamiltonians, and reduction for first-order matrix differential operators”, Funct. Anal. Appl., 14:2 (1980), 146–148  mathnet  crossref  mathscinet  zmath
    7. A. A. Tsvetkov, “On a family of commutative Wick symbols”, Theoret. and Math. Phys., 47:1 (1981), 302–310  mathnet  crossref  mathscinet  isi
    8. V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47  mathnet  crossref  mathscinet  zmath  isi
    9. A. A. Tsvetkov, “Integrals of the nonlinear quantum Schrödinger equation and the trace of the resolvent of the dirac operator”, Funct. Anal. Appl., 15:2 (1981), 152–153  mathnet  crossref  mathscinet  zmath  isi
    10. B. G. Konopelchenko, “Integrable evolution equations: A family of Hamiltonian structures and reductions”, Funct. Anal. Appl., 16:3 (1982), 208–211  mathnet  crossref  mathscinet  zmath  isi
    11. I. M. Gel'fand, I. Ya. Dorfman, “Hamiltonian operators and the classical Yang–Baxter equation”, Funct. Anal. Appl., 16:4 (1982), 241–248  mathnet  crossref  mathscinet  zmath  isi
    12. 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
    13. N. N. Bogolyubov, S. G. Gindikin, A. A. Kirillov, A. N. Kolmogorov, S. P. Novikov, L. D. Faddeev, “Izrail' Moiseevich Gel'fand (on his seventieth birthday)”, Russian Math. Surveys, 38:6 (1983), 145–153  mathnet  crossref  mathscinet  zmath  adsnasa
    14. I. V. Cherednik, “Integrable differential equations and coverings of elliptic curves”, Math. USSR-Izv., 22:2 (1984), 357–377  mathnet  crossref  mathscinet  zmath
    15. V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Math. USSR-Sb., 49:2 (1984), 461–489  mathnet  crossref  mathscinet  zmath
    16. O. I. Mokhov, “The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral”, Russian Math. Surveys, 39:4 (1984), 133–134  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. V. D. Lipovskii, “Hamiltonian structure of the Kadomtsev–Petviashvili–II equation in the class of decreasing Cauchy data”, Funct. Anal. Appl., 20:4 (1986), 282–291  mathnet  crossref  mathscinet  zmath  isi
    18. 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
    19. M. S. Agranovich, “Some asymptotic formulas for elliptic pseudodifferential operators”, Funct. Anal. Appl., 21:1 (1987), 53–56  mathnet  crossref  mathscinet  zmath  isi
    20. S. L. Luk'yanov, “Quantization of the Gel'fand?Dikii brackets”, Funct. Anal. Appl., 22:4 (1988), 255–262  mathnet  crossref  mathscinet  zmath  isi
    21. A. T. Fomenko, “Topological invariants of Liouville integrable Hamiltonian systems”, Funct. Anal. Appl., 22:4 (1988), 286–296  mathnet  crossref  mathscinet  zmath  isi
    22. Theoret. and Math. Phys., 96:2 (1993), 879–973  mathnet  crossref  mathscinet  zmath  isi
    23. P. I. Holod, S. Z. Pakulyak, “The dressing techniques for intermediate hierarchies”, Theoret. and Math. Phys., 103:3 (1995), 668–680  mathnet  crossref  mathscinet  zmath  isi
    24. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. Gesztesy, F, “Uniqueness results for matrix-valued Schrodinger, Jacobi, and Dirac-type operators”, Mathematische Nachrichten, 239 (2002), 103  crossref  isi
    26. S. M. Natanzon, “Witten Solution for the Gelfand–Dikii Hierarchy”, Funct. Anal. Appl., 37:1 (2003), 21–31  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    27. V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, “Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions”, Theoret. and Math. Phys., 144:2 (2005), 1147–1156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. Kanehisa Takasaki, “Hamiltonian Structure of PI Hierarchy”, SIGMA, 3 (2007), 042, 32 pp.  mathnet  crossref  mathscinet  zmath
    29. A. G. Meshkov, “Nonlocal symmetries in two-field divergent evolutionary systems”, Theoret. and Math. Phys., 156:3 (2008), 1268–1279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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