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Algebra i Analiz, 1992, Volume 4, Issue 3, Pages 42–78 (Mi aa321)  

This article is cited in 9 scientific papers (total in 10 papers)

Research Papers

A periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations, and KAM-deformations of finite-gap tori

R. F. Bikbaeva, S. B. Kuksinb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Institute for Information Transmission Problems, Russian Academy of Sciences

Full text: PDF file (1888 kB)

English version:
St. Petersburg Mathematical Journal, 1993, 4:3, 439–468

Bibliographic databases:

Received: 29.01.1992

Citation: R. F. Bikbaev, S. B. Kuksin, “A periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations, and KAM-deformations of finite-gap tori”, Algebra i Analiz, 4:3 (1992), 42–78; St. Petersburg Math. J., 4:3 (1993), 439–468

Citation in format AMSBIB
\Bibitem{BikKuk92}
\by R.~F.~Bikbaev, S.~B.~Kuksin
\paper A~periodic boundary value problem for the sine-Gordon equation, its small Hamiltonian perturbations, and KAM-deformations of finite-gap tori
\jour Algebra i Analiz
\yr 1992
\vol 4
\issue 3
\pages 42--78
\mathnet{http://mi.mathnet.ru/aa321}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1190771}
\zmath{https://zbmath.org/?q=an:0791.35118|0771.35052}
\transl
\jour St. Petersburg Math. J.
\yr 1993
\vol 4
\issue 3
\pages 439--468


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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. R. F. Bikbaev, “Complex Whitham deformations in the problems with “integrable instability””, Theoret. and Math. Phys., 104:3 (1995), 1078–1097  mathnet  crossref  mathscinet  zmath  isi
    2. BOBENKO, AI, “SMALL-AMPLITUDE SOLUTIONS OF THE sine-Gordon EQUATION ON AN INTERVAL UNDER Dirichlet OR Neumann BOUNDARY-CONDITIONS”, Journal of Nonlinear Science, 5:3 (1995), 207  crossref  mathscinet  zmath  adsnasa  isi
    3. BOBENKO, AI, “THE NONLINEAR Klein-Gordon EQUATION ON AN INTERVAL AS A PERTURBED sine-Gordon EQUATION”, Commentarii Mathematici Helvetici, 70:1 (1995), 63  crossref  mathscinet  zmath  isi
    4. V. Yu. Novokshenov, “Whitham Gap Dynamics of the Real-Valued Solution of the Sine-Gordon Equation with Finite-Gap Boundary Conditions”, Funct. Anal. Appl., 30:4 (1996), 246–256  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. R. F. Bikbaev, “Nondegeneracy of amplitude-frequency modulation for finite-gap solutions of integrable nonlinear equations”, Math. Notes, 59:1 (1996), 39–44  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. I. Bobenko, A. M. Il'in, S. Yu. Dobrokhotov, A. R. Its, L. A. Kalyakin, V. B. Matveev, V. Yu. Novokshenov, A. B. Shabat, “Ramil' Faritovich Bikbaev (obituary)”, Russian Math. Surveys, 51:1 (1996), 129–133  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    7. Kuksin, S, “Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrodinger equation”, Annals of Mathematics, 143:1 (1996), 149  crossref  mathscinet  zmath  isi
    8. Rothos, VM, “Existence of homoclinic tubes in the sine-Gordon equation with Hamiltonian perturbation”, Journal of Physics A-Mathematical and General, 32:36 (1999), 6409  crossref  mathscinet  zmath  adsnasa  isi
    9. Shi, YM, “Direct construct of periodic solutions to perturbed Klein-Gordon equations by Newton iteration”, Chinese Annals of Mathematics Series B, 21:3 (2000), 297  crossref  mathscinet  zmath  isi
    10. Kuksin, SB, “KAM-persistence of finite-gap solutions”, Dynamical Systems and Small Divisors, 1784 (2002), 61  mathscinet  isi
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