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SIGMA, 2008, Volume 4, 010, 23 pages (Mi sigma263)  

This article is cited in 6 scientific papers (total in 6 papers)

Global Attraction to Solitary Waves in Models Based on the Klein–Gordon Equation

Alexander I. Komechab, Andrew A. Komechcb

a Faculty of Mathematics, University of Vienna, Wien A-1090, Austria
b Institute for Information Transmission Problems, B. Karetny 19, Moscow 101447, Russia
c Mathematics Department, Texas A\&M University, College Station, TX 77843, USA

Abstract: We review recent results on global attractors of $\mathbf U(1)$-invariant dispersive Hamiltonian systems. We study several models based on the Klein–Gordon equation and sketch the proof that in these models, under certain generic assumptions, the weak global attractor is represented by the set of all solitary waves. In general, the attractors may also contain multifrequency solitary waves; we give examples of systems which contain such solutions.

Keywords: global attractors; solitary waves; solitary asymptotics; nonlinear Klein–Gordon equation; dispersive Hamiltonian systems; unitary invariance

DOI: https://doi.org/10.3842/SIGMA.2008.010

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Full text: http://emis.mi.ras.ru/.../010
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Bibliographic databases:

ArXiv: 0711.0041
MSC: 35B41; 37K40; 37L30; 37N20; 81Q05
Received: November 1, 2007; in final form January 22, 2008; Published online January 31, 2008
Language:

Citation: Alexander I. Komech, Andrew A. Komech, “Global Attraction to Solitary Waves in Models Based on the Klein–Gordon Equation”, SIGMA, 4 (2008), 010, 23 pp.

Citation in format AMSBIB
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\by Alexander I.~Komech, Andrew A.~Komech
\paper Global Attraction to Solitary Waves in Models Based on the Klein--Gordon Equation
\jour SIGMA
\yr 2008
\vol 4
\papernumber 010
\totalpages 23
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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. Tao T., “A global compact attractor for high-dimensional defocusing non-linear Schrodinger equations with potential”, Dyn. Partial Differ. Equ., 5:2 (2008), 101–116  crossref  mathscinet  zmath  isi  elib  scopus
    2. Babin A., Figotin A., “Some mathematical problems in a neoclassical theory of electric charges”, Discrete Contin. Dyn. Syst., 27:4 (2010), 1283–1326  crossref  mathscinet  zmath  isi  elib  scopus
    3. Fontich E., de la Llave R., Sire Ya., “Construction of Invariant Whiskered Tori By a Parameterization Method. Part II: Quasi-Periodic and Almost Periodic Breathers in Coupled Map Lattices”, J. Differ. Equ., 259:6 (2015), 2180–2279  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Prill O., “Asymptotic Stability of the Vacuum Solution For One-Dimensional Nonlinear Klein-Gordon Equations With a Perturbed One-Gap Periodic Potential With and Without An Eigenvalue”, ZAMM-Z. Angew. Math. Mech., 95:8 (2015), 778–821  crossref  mathscinet  zmath  isi  elib  scopus
    5. Komech A., “Attractors of Hamilton nonlinear PDEs”, Discret. Contin. Dyn. Syst., 36:11 (2016), 6201–6256  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. I. Komech, E. A. Kopylova, “Attraktory nelineinykh gamiltonovykh uravnenii v chastnykh proizvodnykh”, UMN, 75:1(451) (2020), 3–94  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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