报告题目:Computation and analysis for the long time dynamics of nonlinear Schrödinger equations

报告人:蔡勇勇 教授(北京师范大学)

报告摘要：

Dispersive PDEs, such as linear/nonlinear Schrödinger equation (NLSE), nonlinear Klein-Gordon equation, nonlinear Dirac equation arise from many different areas, e.g. computational chemistry, plasma physics, quantum mechanics. Recently, the long-time dynamics of such dispersive equations have received much attention. The long time NLSE with small initial data is equivalent to an oscillatory NLSE with $O(1)$ initial data, and such oscillatory PDE is  computational expensive. Here we report recent advances on the numerical methods and analysis for the long time NLSE. In particular, an improved uniform error bound for the time-splitting methods for the long-time NLSE is established. Extensions to other dispersive PDEs will be presented.

报告人简介：

蔡勇勇，北京师范大学教授，本硕就读于北京大学，2012年在新加坡国立大学获得博士学位，2016年入选海外高层次人才引进计划青年项目。他先后在威斯康辛大学麦迪逊分校、马里兰大学帕克分校和普渡大学从事博士后研究工作，2016年至2019年在北京计算科学研究中心任特聘研究员。蔡勇勇教授的研究兴趣是偏微分方程的数值方法及其在量子力学等领域中的应用，在Mathematics of Computation, Journal of Computational Physics和SIAM系列等期刊上发表论文60余篇，多次受邀参加国内外重要学术会议并做相关报告。

报告时间: 2026.5.21(周四) 下午 15:00-16:00

报告地点: 逸夫科研楼1537