Title: Threshold scattering for the focusing NLS with a repulsive Dirac delta potential Show Chinese title

Title: 聚焦NLS的阈值散射与排斥型狄拉克δ势

Abstract: We establish the scattering of solutions to the focusing mass supercritical nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb R}\times{\mathbb R}, \] at the mass-energy threshold, namely, when $E_{\gamma}(u_{0})[M(u_{0})]^{\sigma}=E_{0}(Q)[M(Q)]^{\sigma}$ where $u_{0}\in H^{1}({\mathbb R})$ is the initial data, $Q$ is the ground state of the free NLS on the real line ${\mathbb R}$, $E_{\gamma}$ is the energy, $M$ is the mass and $\sigma=(p+3)/(p-5)$. We also prove failure of the uniform space-time bounds at the mass-energy threshold. Show Chinese abstract

Abstract: 我们建立聚焦质量超临界非线性薛定谔方程在质量-能量阈值处的散射，即当\[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb R}\times{\mathbb R}, \]为排斥狄拉克 delta 势时，$E_{\gamma}(u_{0})[M(u_{0})]^{\sigma}=E_{0}(Q)[M(Q)]^{\sigma}$其中$u_{0}\in H^{1}({\mathbb R})$是初始数据，$Q$是实线上自由 NLS 的基态，${\mathbb R}$，$E_{\gamma}$是能量，$M$是质量且$\sigma=(p+3)/(p-5)$。 我们还证明了在质量-能量阈值处一致时空界限的失效。