报告名称：Defocusing NLS equation with a nonzero background: Painleve asymptotics in two transition regions

主讲人：范恩贵 教授

邀请人：黄丽丽 助理研究员

时间：2023年7月6日   10:00

地点：十大网投正规信誉官网326会议室

主办单位：十大网投正规信誉官网

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.

专家简介

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。