报告题目: Computational methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity

报告人：包维柱，新加坡国立大学

报告时间：2026年4月30日（周四），10:00-12:00

报告地点：数学楼2-3会议室

报告摘要: In this talk, we begin with the nonlinear Schroedinger equation (NLSE) with different low regularity potentials and nonlinearities arising from modeling and simulation for quantum physics and chemistry, nonlinear/quantum optics, and quantum information and computation, etc. Optimal error bounds for time-splitting methods and exponential wave integrators are established for the NSLE under the proper regularity assumption on its solution determined by the low regularity potential and nonlinearity. Then we propose a novel symmetric and explicit Gautschi-type exponential wave integrator (sEWI) for the NLSE with low regularity potential and nonlinearity, and establish its optimal error estimates under various regularity assumptions on potential and nonlinearity. Extensions to the NLSE with singular potentials and nonlinearities are presented. Finally, extensions to other dispersive PDEs with low regularity potential and nonlinearity are discussed. This talk is based on joint works with Remi Carles, Yue Feng, Bo Lin, Ying Ma, Chunmei Su, Qinglin Tang and Chushan Wang.

报告人简介：Weizhu BAO is a Professor at the Department of Mathematics, National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty positions at Tsinghua University, Imperial College, Georgia Institute of Technology and the University of Wisconsin at Madison. His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, analysis and computation for problems from physics, chemistry, biology and engineering sciences. He has made significant contributions in modeling and simulation of Bose-Einstein condensation, solid-state dewetting and geometric PDEs; and in multiscale methods and analysis for highly oscillatory PDEs. He had been on the Editorial Board of SIAM Journal on Scientific Computing during 2009-2014 and is currently on the Editorial Board of SIAM Journal on Numerical Analysis. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. Weizhu Bao was an invited speaker at the ICM 2014 in Seoul. He is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics and the Singapore National Academy of Science.