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

By Andrew A. Komech and Alexander I. Komech

Abstract

We review recent results on global attractors of 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

Topics: global attractors, solitary waves, solitary asymptotics, nonlinear Klein-Gordon equation, dispersive Hamiltonian systems, unitary invariance, Mathematics, QA1-939, Science, Q, DOAJ:Mathematics, DOAJ:Mathematics and Statistics
Publisher: National Academy of Science of Ukraine
Year: 2008
DOI identifier: 10.3842/SIGMA.2008.010
OAI identifier: oai:doaj.org/article:c0bbfa134dbb427f9cbe9c9861ee3e5c
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