报告题目:

Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations

报告人:新加坡国立大学数学系 包维柱教授

北京时间：2022年12月7日 下午16：00-17：00

腾讯会议：899149128

报告内容简介：

In this talk, I begin wtih the (nonlinear) Schrodinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics, soliton solutions and semiclassical limits. Different numerical methods will be presented including finite difference time domain (FDTD) methods and time-splitting spectral (TSSP) method, and their error estimates and comparison will be discussed. Extensions to NLSE/GPE with an angular momentum rotation term, non-local dipole-dipole interaction, multi-component and logarithmic nonlinearity will be presented. Applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated. Finally, I will report our very recent results of energy regularization methods for NLSE with logarithmic nonlinearity and improved uniform error bounds on TSSP for the long-time dynamics of NLSE by using the regularization compensation oscillatory (RCO) technique.

报告人包维柱教授简介：

Professor Weizhu BAO is a Professor at 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 in UK, Georgia Institute of Technology and University of Wisconsin at Madison in USA. He joined NUS as an Assistant Professor in 2000 and was promoted to Professor in 2009. He had been appointed as the Provost's Chair Professorship at NUS during 2013-2016. 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 of Numerical Analysis. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. He has been invited to give plenary and/or invited talks in many international conferences including an Invited Speaker at the International Congress of Mathematicians (ICM) in 2014. He was elected a Fellow of the American Mathematical Society (AMS Fellow), a Fellow of the Society of Industrial and Applied Mathematics (SIAM Fellow) and a Fellow of Singapore National Academy of Science (SNAS Fellow) in 2022.

主办单位：中国人民大学数学学院，邀请人：柯媛元