4 problems

Let $u$ solve the one-dimensional $L^2$-critical nonlinear Schrödinger equation with repulsive delta potential $u<0$, with initial data $u0in H^1(mathbb{R})$ satisfying … where…

Conjecture on the transmission exponent. The exponent in this asymptotic is exactly

Let $z=z(t)$ denote the center position of a solitary wave in a global solution of the damped nonlinear Klein–Gordon equation with delta potential, and let $\sigma\in\{0,1\}$ and…

Let $u$ solve the one-dimensional nonlinear Schrödinger equation with a repulsive delta potential of strength $\Gamma$, and consider even two-soliton solutions whose solitons separ…