6 problems

Let the nonlinear Klein–Gordon (NLKG) equation be the relativistic analogue of the nonlinear Schrödinger equation, and consider its corresponding stationary soliton solutions. Chen…

Let $\Omega$ be a regular polygon with at least seven edges and a center, in the setting of the damped nonlinear Klein–Gordon equation and the multi-soliton construction described…

Consider a Hamiltonian nonlinear perturbation of the linear dispersive Klein–Gordon equation with a discrete eigenfrequency $\omega$ and continuous spectral threshold $m$, in the w…

Phase-transition conjecture. The stationary solution $u(t,x)=Q$ belongs to the boundary of the scattering domain. The ground state is the distinguished stationary threshold separat…

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…