Global attraction to solitary waves for Klein–Gordon equation with mean field interaction Academic Article uri icon

abstract

  • We consider a U (1)-invariant nonlinear Klein-Gordon equation in dimension n ≥ 1, 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 t → ± ∞ to the two-dimensional set of all "nonlinear eigenfunctions" of the form φ{symbol} (x) e- i ω t. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation. © 2008 Elsevier Masson SAS. All rights reserved.

author list (cited authors)

  • Komech, A., & Komech, A.

citation count

  • 17

publication date

  • May 2009