报告题目 (Title)：非零背景下聚焦NLS方程：在两个过渡区域下的Painleve渐近（Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions）

报告人 (Speaker)：范恩贵 教授（复旦大学）

报告时间 (Time)：2023年10月16日(周一) 14:00

报告地点 (Place)：校本部F309

邀请人(Inviter)：夏铁成 教授

主办部门：理学院数学系

报告摘要：We address the Painleve asymptotics of the solution in two transition regionsfor the defocusing nonlinear Schrodinger (NLS) equation with finite density initial data. The key to prove this result is the formulation and analysis of a Riemann-Hilbert problem associated with the Cauchy problem for the defocusing NLS equation. With the Dbar generalization of the Deift-Zhou nonlinear steepest descent method and double scaling limit technique, in two transition regions, we find that the leading order approximation to the solution of the defocusing NLS equation can be expressed in terms of the Hastings-McLeod solution of the Painleve II equation in the generic case, while Ablowitz-Segur solution in the non-generic case.