一、报告题目：Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions
二、报告人： 复旦大学范恩贵教授
三、报告时间：2023年7月7日星期五9：30-10：30
四、报告地点：启智楼80602
五、报告摘要：
We address the Painleve asymptotics of the solution in two transition regions for 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.
六、报告人简介：
范恩贵，复旦大学教授、博士生导师,上海市曙光学者，主要研究方向是孤立子理论、可积系统、Riemann-Hilbert问题、正交多项式和随机矩阵理论；主持国家自然科学基金、上海曙光计划等多项研究课题。 在 《Adv. Math. 》、 《Comm. Math. Phys.》、《SIAM J. Math. Anal.》、《J. Diff. Equ.》等国际重要期刊发表论文100余篇。应邀访问美国密苏里大学、日本京都大学等。曾获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖。
