学术报告报告题目：The universality of the semi-classical sine-Gordon equation at the gradient catastrophe
报 告人：Bingling-Lu (University of Bremen)
报告时间：2021年 9月 18日（星期 六）下午 3：00-4：00
报告地点：腾讯会议，会议号：188 881 201
邀 请人：凌黎明教授
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数学学院
2021年 9 月 13 日
报告摘要：We study the semi-classical sine-Gordon equation with pure impulse initial data below the threshold of rotation:
A dispersively-regularized shock forms in finite time. Using Riemann–Hilbert analysis, we rigorously studied the asymptotics near a certain gradient catastrophe. In accordance with a conjecture made by Dubrovin et. al., the asymptotics in the this region is universally (insensitive to initial condition) described by the tritronquee solution to the Painleve-I equation. Furthermore, we are able to universally characterize the shapes of the spike-like local structures (rogue wave on periodic background) on top of the poles of the tritronqu\’ee solution.
报告人简介：Bingling Lu, 本科毕业于上海交通大学，博士毕业于University of Michigan, 博士毕业之后在台湾大学中央研究院从事博士后研究，现任职于University of Bremen. Bingling-Lu长期从事于Riemann-Hilbert渐近性的研究，尤其是半经典极限的分析。 在数学权威期刊“Communications on Pure and Applied Mathematics”发表文章。