On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator

Details On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator

2006-08-24

arxiv.org/abs/math/0608605v1

Comptes Rendus Mathematique Volume 343, Issue 2, 15 July 2006, Pages 111-114

Mathematics

Analysis of PDEs

5 pages, 1 figure

Scientific paper

The long-time asymptotics is analyzed for all finite energy solutions to a
model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the
nonlinearity concentrated at a point. Our main result is that each finite
energy solution converges as $t\to\pm\infty$ to the set of ``nonlinear
eigenfunctions'' $\psi(x)e\sp{-i\omega t}$.

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