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MiS Preprint

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

Alexander Komech and Andrew Komech


We consider a $\mathbf{U}(1)$-invariant nonlinear Klein-Gordon equation in dimension $n\ge 1$, 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 $t\to\pm\infty$ to the two-dimensional set of all "nonlinear eigenfunctions" of the form $\phi(x)e^{-i\omega t}$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.

Jul 30, 2007
Jul 30, 2007

Related publications

2009 Repository Open Access
Alexander Komech and Andrew Komech

Global attraction to solitary waves for Klein-Gordon equation with mean field interaction

In: Annales de l'Institut Henri Poincaré / C, 26 (2009) 3, pp. 855-868