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

发布时间:2025-10-30 作者: 浏览次数:
Speaker: 包维柱 DateTime: 2025年11月5日(周三)下午14:00-16:00
Brief Introduction to Speaker:

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。


Place: 腾讯会议:587-916-808
Abstract: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 im...