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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 1, Pages 41–63 (Mi izv1167)  

This article is cited in 7 scientific papers (total in 7 papers)

Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems

S. B. Kuksin


Abstract: A theorem on preservation of quasiperiodic solutions under small perturbations of the Hamiltonian is proved for a certain class of infinite-dimensional Hamiltonian systems. Hamiltonian perturbations of the one-dimensional Schrödinger equation are considered as examples.
Bibliography: 10 titles.

Full text: PDF file (2583 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:1, 39–62

Bibliographic databases:

UDC: 517.957
MSC: Primary 58F05, 58F30, 58F27; Secondary 35J10, 70H99
Received: 29.01.1986

Citation: S. B. Kuksin, “Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems”, Izv. Akad. Nauk SSSR Ser. Mat., 52:1 (1988), 41–63; Math. USSR-Izv., 32:1 (1989), 39–62

Citation in format AMSBIB
\Bibitem{Kuk88}
\by S.~B.~Kuksin
\paper Perturbation of quasiperiodic solutions of infinite-dimensional Hamiltonian systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 1
\pages 41--63
\mathnet{http://mi.mathnet.ru/izv1167}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=936522}
\zmath{https://zbmath.org/?q=an:0667.58060|0662.58036}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 1
\pages 39--62
\crossref{https://doi.org/10.1070/IM1989v032n01ABEH000733}


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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, “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
    2. S. B. Kuksin, “Conservative perturbations of infinite-dimensional linear systems depending on a vector parameter”, Funct. Anal. Appl., 23:1 (1989), 62–63  mathnet  crossref  mathscinet  zmath  isi
    3. R Cirelli, L Pizzocchero, Nonlinearity, 3:4 (1990), 1057  crossref  mathscinet  zmath  isi
    4. G. R. W. Quispel, M. B. Sevryuk, “KAM theorems for the product of two involutions of different types”, Chaos, 3:4 (1993), 757  crossref  mathscinet  zmath  adsnasa
    5. Alejandro Luque, Jordi Villanueva, “A KAM theorem without action-angle variables for elliptic lower dimensional tori”, Nonlinearity, 24:4 (2011), 1033  crossref
    6. Hongzi Cong, Meina Gao, Jianjun Liu, “Long time stability of KAM tori for nonlinear wave equation”, Journal of Differential Equations, 2015  crossref
    7. Jie Liu, Jianguo Si, “Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing”, J. Math. Phys, 56:3 (2015), 032702  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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