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.
Cite this article
Alexander Komech, Andrew Komech, Global attraction to solitary waves for Klein–Gordon equation with mean field interaction. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 855–868DOI 10.1016/J.ANIHPC.2008.03.005