报告题目：Ground states and dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations

主 讲 人：包维柱 教授

单 位：新加坡国立大学

时 间：5月9日15:00

ZOOM ID：975 2011 3597

密 码：123456

摘 要：

In this talk, I begin with a brief derivation of the nonlinear Schrodinger/Gross-Pitaevskii equations (NLSE/GPE) from Bose-Einstein condensates (BEC) and/or nonlinear optics. Then I will present some mathematical results on the existence and uniqueness as well as non-existence of the ground states of NLSE/GPE under different external potentials and parameter regimes. Dynamical properties of NLSE/GPE are then discussed, which include conservation laws, soliton solutions, well-posedness and/or finite time blowup. Efficient and accurate numerical methods will be presented for computing numerically the ground states and dynamics. Extension to NLSE/GPE with an angular momentum rotation term and/or non-local dipole-dipole interaction will be presented. Finally, applications to collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.

简 介：

包维柱教授1995年博士毕业于清华大学，现为新加坡国立大学数学系provost讲席教授，2013年获冯康科学计算奖，2014年应邀在韩国举行的第26届国际数学家大会上作45分钟邀请报告，担任包括SIAM Journal on Scientific Computing等多个国际期刊杂志编委。包维柱教授长期从事科学与工程计算研究，主要工作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。特别是在Bose-Einstein凝聚的数值方法及应用、高震荡色散类偏微分方程的多尺度算法和分析、无界区域上科学和工程问题的计算等方面取得了多个重要进展。