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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 010, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.010 (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
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DOI: https://doi.org/10.3842/SIGMA.2008.010
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.
Received: November 1, 2007; in final form January 22, 2008; Published online January 31, 2008
Bibliographic databases:
Document Type: Article
MSC: 35B41; 37K40; 37L30; 37N20; 81Q05
Language: English
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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