2 problems

The discrete nonlinear Klein–Gordon equation is … Its quasi-stationary solutions have the form $u(t)=\cos(\mu t+\nu)\alpha_\mu$, where $\mu$ and $\nu$ are parameters and…

Let $\mu=\pm1$. Let $(u_0,u_1)\in H^1_x\times L^2_x$. In the focusing case, assume additionally that $M(u_0)<M(Q)$ and $E(u_0,u_1)<E(Q)$, where $Q$ is the ground state. A solution…