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

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

2007-10-31

arxiv.org/abs/0711.0041v6

SIGMA 4 (2008), 010, 23 pages

Mathematics

Analysis of PDEs

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.010

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.

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