Global attraction to solitary waves for Klein-Gordon equation with mean field interaction

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We consider a U(1)-invariant nonlinear Klein-Gordon equation in dimension one or larger, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic assumptions, each solution converges (as time goes to infinity) to the two-dimensional set of all ``nonlinear eigenfunctions'' of the form $ϕ(x)e\sp{-iωt}$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.

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Mathematical Physics, 37K; 35B41; 35L; 35Q; 81

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http://salesiana.dossiersoluciones.com/handle/123456789/156503

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1131
 http://arxiv.org/abs/0708.1131

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arXiv