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Uspekhi Mat. Nauk, 1986, Volume 41, Issue 5(251), Pages 109–152 (Mi umn2209)  

This article is cited in 15 scientific papers (total in 15 papers)

The method of Poincaré normal forms in problems of integrability of equations of evolution type

N. V. Nikolenko


Full text: PDF file (2232 kB)
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English version:
Russian Mathematical Surveys, 1986, 41:5, 63–114

Bibliographic databases:

UDC: 517.9
MSC: 34G20, 34A12, 46B28
Received: 12.02.1984

Citation: N. V. Nikolenko, “The method of Poincaré normal forms in problems of integrability of equations of evolution type”, Uspekhi Mat. Nauk, 41:5(251) (1986), 109–152; Russian Math. Surveys, 41:5 (1986), 63–114

Citation in format AMSBIB
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\by N.~V.~Nikolenko
\paper The~method of Poincar\'e normal forms in problems of integrability of equations of evolution type
\jour Uspekhi Mat. Nauk
\yr 1986
\vol 41
\issue 5(251)
\pages 109--152
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\transl
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 5
\pages 63--114
\crossref{https://doi.org/10.1070/RM1986v041n05ABEH003423}
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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. S. B. Kuksin, “Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum”, Funct. Anal. Appl., 21:3 (1987), 192–205  mathnet  crossref  mathscinet  zmath  isi
    2. S. B. Kuksin, “Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems”, Math. USSR-Izv., 32:1 (1989), 39–62  mathnet  crossref  mathscinet  zmath
    3. A. V. Mishchenko, D. Ya. Petrina, “Linearization and exact solutions of a class of Boltzmann equations”, Theoret. and Math. Phys., 77:1 (1988), 1096–1109  mathnet  crossref  mathscinet  zmath  isi
    4. Gilberto Flores, “The stable manifold of the standing wave of the Nagumo equation”, Journal of Differential Equations, 80:2 (1989), 306  crossref
    5. C. Eugene Wayne, “Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory”, Comm Math Phys, 127:3 (1990), 479  crossref  mathscinet  zmath  isi
    6. H. P. McKean, J. Shatah, “The nonlinear Schrödinger equation and the nonlinear heat equation reduction to linear form”, Comm Pure Appl Math, 44:8-9 (1991), 1067  crossref  mathscinet  zmath  isi
    7. Kening Lu, “A Hartman-Grobman theorem for scalar reaction-diffusion equations”, Journal of Differential Equations, 93:2 (1991), 364  crossref
    8. Bernd Aulbach, Barnabas M. Garay, “Partial linearization for noninvertible mappings”, Z angew Math Phys, 45:4 (1994), 505  crossref  mathscinet  zmath  isi
    9. L. R. Volevich, A. R. Shirikyan, “Local dynamics for high-order semilinear hyperbolic equations”, Izv. Math., 64:3 (2000), 439–485  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Percy Deift, Xin Zhou, “Perturbation theory for infinite-dimensional integrable systems on the line. A case study”, Acta Math, 188:2 (2002), 163  crossref  mathscinet  zmath  isi
    11. Yanguang C Li, “Existence of chaos in evolution equations”, Mathematical and Computer Modelling, 36:11-13 (2002), 1211  crossref
    12. Ranchao Wu, Jianhua Sun, “Homoclinic orbits for perturbed coupled nonlinear Schrödinger equations”, Chaos, Solitons & Fractals, 29:2 (2006), 423  crossref
    13. D. Bambusi, J.-M. Delort, B. Grébert, J. Szeftel, “Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds”, Comm Pure Appl Math, 60:11 (2007), 1665  crossref  mathscinet  zmath  isi  elib
    14. Jiansheng Geng, Jiangong You, Zhiyan Zhao, “Localization in One-dimensional Quasi-periodic Nonlinear Systems”, Geom. Funct. Anal, 2014  crossref
    15. Zhihua Liu, Pierre Magal, Shigui Ruan, “Normal forms for semilinear equations with non-dense domain with applications to age structured models”, Journal of Differential Equations, 2014  crossref
  • Успехи математических наук Russian Mathematical Surveys
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