报告题目：Computing the action ground state for the rotating nonlinear Schrödinger equation
报告时间：2024年5月25日（星期六）上午8:40-9:40
会议地点：藕舫楼629
报告人：袁永军 教授
主持人：王廷春 教授
报告摘要：In this talk, the computations of the action ground state for a rotating nonlinear Schrödinger equation are considered. It reads as a minimization of the action functional under the Nehari constraint. In the focusing case, we identify an equivalent formulation of the problem which simplifies the constraint. Based on it, we propose a normalized gradient flow method with asymptotic Lagrange multiplier and establish the energy-decaying property. Popular optimization methods are also applied to gain more efficiency. In the defocusing case, we prove that the ground state can be obtained by the unconstrained minimization. Then the direct gradient flow method and unconstrained optimization methods are applied. Numerical experiments show the convergence and accuracy of the proposed methods in both cases, and comparisons on the efficiency are discussed. Finally, the relation between the action and the energy ground states are numerically investigated.
专家简介：袁永军，男，博士，教授，湖南省青年芙蓉学者。2007年本科毕业于湖南师范大学大学数学与应用数学专业，2012年博士毕业于湖南师范大学计算数学专业， 2012年至2015年先后在北京计算科学研究中心和新加坡国立大学从事博士后研究工作，2015年11月进入湖南师范大学工作至今。主要从事非线性偏微分方程多解计算和玻色-爱因斯坦凝聚数值模拟方面研究，部分工作发表在Mathematics of Computation, SIAM Journal on Scientific Computing, Physical Review Letters, Journal of Computational Physics和Physical Review A等杂志。主持国家自然科学基金青年基金项目和面上项目各1项。
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数学与统计学院
2024年5月20日
