Global attraction to solitary waves for Klein-Gordon equation with mean field interaction
نویسندگان
چکیده
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(x)e−iωt . This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.
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