Scattering for the beam equation

In this paper, we study the scattering for the nonlinear beam equation $u_{tt}+\Delta^2u+mu+\mu |u|^{p-1}u=0$. Our results include two aspects. In the defocusing case we show that the scattering holds for $d=1$, which extends the result in \cite{Pau-Beam} to one dimension. In the focusing case, we show that the scattering holds in $\R^d (d\ge 1)$ when the energy $E(u_0,u_1)