On global attraction to quantum stationary states III. Klein-Gordon equation with mean field interaction
Alexander Komech and Andrew Komech
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Submission date: 30. Jul. 2007
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
with the following different title: Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
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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.