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

Simple item page
dc.creatorKomech, Alexander
dc.creatorKomech, Andrew
dc.date2007-08-08
dc.date2008-03-11
dc.date.accessioned2026-07-07T09:25:44Z
dc.date.available2026-07-07T09:25:44Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0708.1131
dc.identifierhttp://arxiv.org/abs/0708.1131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156503
dc.subjectMathematical Physics
dc.subject37K; 35B41; 35L; 35Q; 81
dc.titleGlobal attraction to solitary waves for Klein-Gordon equation with mean field interaction
dc.typetext

Files

Collections

arXiv