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Russian Mathematical Surveys, 1986, Volume 41, Issue 5, Pages 63–114
DOI: https://doi.org/10.1070/RM1986v041n05ABEH003423
(Mi rm2209)
 

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

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

N. V. Nikolenko
References:
Received: 12.02.1984
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 34G20, 34A12, 46B28
Language: English
Original paper language: Russian
Citation: N. V. Nikolenko, “The method of Poincaré normal forms in problems of integrability of equations of evolution type”, Russian Math. Surveys, 41:5 (1986), 63–114
Citation in format AMSBIB
\Bibitem{Nik86}
\by N.~V.~Nikolenko
\paper The~method of Poincar\'e normal forms in problems of integrability of equations of evolution type
\jour Russian Math. Surveys
\yr 1986
\vol 41
\issue 5
\pages 63--114
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\crossref{https://doi.org/10.1070/RM1986v041n05ABEH003423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=878327}
\zmath{https://zbmath.org/?q=an:0632.35026}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1986RuMaS..41...63N}
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Linking options:
  • https://www.mathnet.ru/eng/rm2209
  • https://doi.org/10.1070/RM1986v041n05ABEH003423
  • https://www.mathnet.ru/eng/rm/v41/i5/p109
  • This publication is cited in the following 28 articles:
    1. Toshiki Kondo, Mamoru Okamoto, “Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle”, Partial Differ. Equ. Appl., 6:2 (2025)  crossref
    2. Michela Procesi, Laurent Stolovitch, “About Linearization of Infinite-Dimensional Hamiltonian Systems”, Commun. Math. Phys., 394:1 (2022), 39  crossref
    3. Zhihua Liu, Pierre Magal, “Bogdanov–Takens bifurcation in a predator–prey model with age structure”, Z. Angew. Math. Phys., 72:1 (2021)  crossref
    4. Dario Bambusi, Laurent Stolovitch, “Convergence to Normal Forms of Integrable PDEs”, Commun. Math. Phys., 376:2 (2020), 1441  crossref
    5. Luca Biasco, Jessica Elisa Massetti, Michela Procesi, “An Abstract Birkhoff Normal Form Theorem and Exponential Type Stability of the 1d NLS”, Commun. Math. Phys., 375:3 (2020), 2089  crossref
    6. Pierre Magal, Shigui Ruan, Applied Mathematical Sciences, 201, Theory and Applications of Abstract Semilinear Cauchy Problems, 2018, 249  crossref
    7. Jiansheng Geng, Jiangong You, Zhiyan Zhao, “Localization in One-dimensional Quasi-periodic Nonlinear Systems”, Geom. Funct. Anal, 2014  crossref
    8. 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
    9. Dario Bambusi, Mathematics of Complexity and Dynamical Systems, 2012, 1337  crossref
    10. Dario Bambusi, Encyclopedia of Complexity and Systems Science, 2009, 6709  crossref
    11. Dario Bambusi, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2009, 229  crossref
    12. 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
    13. Ranchao Wu, Jianhua Sun, “Homoclinic orbits for perturbed coupled nonlinear Schrödinger equations”, Chaos, Solitons & Fractals, 29:2 (2006), 423  crossref
    14. D. Bambusi, B. Grébert, “Birkhoff normal form for partial differential equations with tame modulus”, Duke Math. J., 135:3 (2006)  crossref
    15. 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
    16. Yanguang C Li, “Existence of chaos in evolution equations”, Mathematical and Computer Modelling, 36:11-13 (2002), 1211  crossref
    17. 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
    18. V. D. Belousov, V. E. Plisko, E. B. Yanovskaya, D. D. Sokolov, S. Yu. Maslov, A. A. Bukhshtab, V. I. Nechaev, V. M. Paskonov, V. A. Artamonov, A. V. Prokhorov, N. V. Efimov, B. V. Khvedelidze, I. V. Dolgachev, V. A. Iskovskikh, A. B. Ivanov, V. T. Bazylev, A. V. Arkhangel'skiǐ, A. A. Sapozhenko, P. S. Saltan, P. S. Soltan, V. A. Chuyanov, M. Sh. Farber, S. V. Shvedenko, V. P. Petrenko, I. P. Mysovskikh, V. A. Trenogin, M. K. Samarin, Yu. A. Kuznetsov, E. D. Solomentsev, M. S. Nikulin, L. D. Kudryavtsev, V. N. Latyshev, D. V. Anosov, A. L. Shmel'kin, L. N. Shevrin, L. V. Kuz'min, V. L. Popov, D. V. Alekseevskiǐ, V. N. Remeslennikov, P. L. Dobrushin, V. V. Prelov, G. S. Khovanskiǐ, A. L. Onishchik, A. K. Tolpygo, L. A. Sidorov, L. A. Bokut', A. Ya. Kiruta, E. A. Palyutin, A. D. Taǐmanov, E. I. Vilkas, V. V. Rumyantsev, E. G. D'yakonov, A. F. Shapkin, L. E. Evtushik, V. I. Sobolev, V. M. Starszhinskiǐ, S. J. Pokhozhaev, V. G. Karmanov, Encyclopaedia of Mathematics, 1995, 67  crossref
    19. Bernd Aulbach, Barnabas M. Garay, “Partial linearization for noninvertible mappings”, Z angew Math Phys, 45:4 (1994), 505  crossref  mathscinet  zmath  isi
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
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