Chen–Fröhlich–Walcher metastability conjecture for noncommutative Klein–Gordon solitons

The discrete nonlinear Klein–Gordon equation is

$$-\partial_t^2u=L_0u-u^p,\qquad 1<p\in\mathbb{Z}.$$

Its quasi-stationary solutions have the form $u(t)=\cos(\mu t+\nu)\alpha_\mu$, where $\mu$ and $\nu$ are parameters and $\alpha_\mu$ is the corresponding localized profile. Chen–Fröhlich–Walcher's metastability conjecture. Solutions of the discrete real nonlinear Klein–Gordon equation that begin close to $u(t)=\cos(\mu t+\nu)\alpha_\mu$ are metastable resonance functions. The conjecture concerns localized solutions whose coupling to radiation produces a resonance with a long, rather than immediate, decay time; the source gives no resolution.