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报告题目: 杰出学者讲坛(七十一):Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
报 告 人: Professor Weizhu Bao
报告人所在单位: Department of Mathematics, National University of Singapore
报告日期: 2023-06-20
报告时间: 9:00-10:00
报告地点: 光华东主楼2201
   
报告摘要:

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.

杰出学者讲坛七十一.jpg

   
本年度学院报告总序号: 13

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