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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 396–412 (Mi msb1750)  

This article is cited in 17 scientific papers (total in 18 papers)

Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation

S. B. Kuksin


Abstract: A perturbation theory is constructed for quasiperiodic solutions of nonlinear conservative systems of large and of infinite dimension.
Bibliography: 17 titles.

Full text: PDF file (891 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 397–413

Bibliographic databases:

UDC: 517.957
MSC: Primary 58F07, 35B20; Secondary 35Q20
Received: 07.09.1987

Citation: S. B. Kuksin, “Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg–de Vries equation”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 396–412; Math. USSR-Sb., 64:2 (1989), 397–413

Citation in format AMSBIB
\Bibitem{Kuk88}
\by S.~B.~Kuksin
\paper Perturbation theory for quasiperiodic solutions of infinite-dimensional Hamiltonian systems, and its application to the Korteweg--de~Vries equation
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 3(7)
\pages 396--412
\mathnet{http://mi.mathnet.ru/msb1750}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=959490}
\zmath{https://zbmath.org/?q=an:0678.58037|0657.58033}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 397--413
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003316}


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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. A.I. Bobenko, S.B. Kuksin, “Finite-gap periodic solutions of the KdV equation are non-degenerate”, Physics Letters A, 161:3 (1991), 274  crossref
    2. P. Loshak, “Canonical perturbation theory via simultaneous approximation”, Russian Math. Surveys, 47:6 (1992), 57–133  mathnet  crossref  mathscinet  adsnasa  isi
    3. Sergej B. Kuksin, “An infinitesimal Liouville-Arnold theorem as a criterion of reducibility for variational Hamiltonian equations”, Chaos, Solitons & Fractals, 2:3 (1992), 259  crossref  elib
    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. Bikbaev R., “Shock-Waves in the Modified Korteweg-de Vries-Burgers Equation”, J. Nonlinear Sci., 5:1 (1995), 1–10  crossref  mathscinet  zmath  adsnasa  isi
    6. A V Babin, L A Bunimovich, Nonlinearity, 9:4 (1996), 853  crossref  mathscinet  zmath  isi
    7. Bikbaev R., “The Frequency Map for the Integrable Nonlinear Schrodinger Equation and Geometry of Zeros of Abelian Differentials”, Russ. J. Math. Phys., 4:1 (1996), 3–12  mathscinet  zmath  isi
    8. Bourgain J., “Quasi-Periodic Solutions of Hamiltonian Perturbations of 2D Linear Schrodinger Equations”, Ann. Math., 148:2 (1998), 363–439  crossref  mathscinet  zmath  isi
    9. Albeverio S., Khrennikov A., Smolyanov O., “A Local Liouville Theorem for Infinite-Dimensional Hamilton-Dirac Systems”, Russ. J. Math. Phys., 9:2 (2002), 123–139  mathscinet  zmath  isi
    10. Luigi Chierchia, Dingbian Qian, “Moser's theorem for lower dimensional tori”, Journal of Differential Equations, 206:1 (2004), 55  crossref
    11. Zhang D., Xu J., “On Elliptic Lower Dimensional Tori for Gevrey-Smooth Hamiltonian Systems Under Russmann's Non-Degeneracy Condition”, Discret. Contin. Dyn. Syst., 16:3 (2006), 635–655  crossref  mathscinet  zmath  isi
    12. Henk W Broer, Heinz Hanßmann, Jun Hoo, “The quasi-periodic Hamiltonian Hopf bifurcation”, Nonlinearity, 20:2 (2007), 417  crossref  mathscinet  zmath  isi  elib
    13. Kappeler T., Poeschel J., “On the Well-Posedness of the Periodic KdV Equation in High Regularity Classes”, Hamiltonian Dynamical Systems and Applications, NATO Science for Peace and Security Series B - Physics and Biophysics, ed. Craig W., Springer, 2008, 431–441  crossref  mathscinet  zmath  isi
    14. Chierchia L., Pinzari G., “The Planetary N-Body Problem: Symplectic Foliation, Reductions and Invariant Tori”, Invent. Math., 186:1 (2011), 1–77  crossref  mathscinet  zmath  adsnasa  isi
    15. Antonio Giorgilli, Ugo Locatelli, Marco Sansottera, “On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems”, Celest Mech Dyn Astr, 2014  crossref
    16. Huang Guan, Sergei Kuksin, “The KdV equation under periodic boundary conditions and its perturbations”, Nonlinearity, 27:9 (2014), R61  crossref
    17. Boris Dubrovin, Tamara Grava, Christian Klein, Antonio Moro, “On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations”, J Nonlinear Sci, 2015  crossref
    18. C. Wayne, T. Kappeler, G. Kokarev, W. Craig, A. Piatnitsky, I. Chueshov, A. Shirikyan, L. H. Eliasson, “Sergei Borisovich Kuksin (on his 60th birthday)”, Russian Math. Surveys, 71:1 (2016), 167–173  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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