On global attraction to quantum stationary states III. Klein-Gordon equation with mean field interaction

Alexander Komech and Andrew Komech

Contact the author: Please use for correspondence this email.
Submission date: 30. Jul. 2007
Pages: 15
published in: Annales de l'Institut Henri Poincaré / C, 26 (2009) 3, p. 855-868 
DOI number (of the published article): 10.1016/j.anihpc.2008.03.005
Bibtex
with the following different title: Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
Download full preprint: PDF (165 kB), PS ziped (132 kB)

Abstract:
We consider a -invariant nonlinear Klein-Gordon equation in dimension , 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 to the two-dimensional set of all ``nonlinear eigenfunctions'' of the form . This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.