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

Alexander Komech·Andrew Komech
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Abstract

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'' $ψ(x)e\sp{-iωt}$.

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Alexander Komech, Andrew Komech. 2006-08-24. On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator. https://arxiv.org/abs/math/0608605

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