报告人：包维柱 教授

时间：2025年11月5日（周三）下午14:00-16:00

地点：腾讯会议：150-589-94

摘要：In this talk, I begin wtih the (nonlinear) Schroedinger/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 report our very recent results of energy regularization methodsfor 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 as well as error estimateson numerical methods for NLSE with low regularity potential and nonlinearity.

报告人简介：包维柱教授现为新加坡国立大学数学系教授，理学院副院长，新加坡科学院院士，美国数学会会士（AMS Fellow），美国工业与应用数学学会会士（SIAM Fellow）。2013年获冯康科学计算奖，2014年受邀在国际数学家大会上作45分钟邀请报告。包维柱教授长期从事科学与工程计算研究，研究涉及偏微分方程数值方法及其在量子物理、流体和材料中的应用。