报告题目：Darboux Transformations, Higher-Order Rational Solitons and Rogue Wave Solutions for a (2 + 1)-Dimensional Nonlinear Schrodinger Equation
报告人：   李彪  教授 宁波大学
主持人：    陈勇 教授
报告时间：2019年3月17日  周日16:00-17:00
报告地点：中北校区数学馆东202
 

报告摘要：
By Taylor expansion of Darboux matrix, a new generalized Darboux transformations (DTs) for a (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation is derived , which can be reduced to two (1 + 1)-dimensional equation: a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave (RW) solutions are constructed by its (1;N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.

报告人简介：
李彪教授，男，博士，博士后。主要从事数学物理，Lie群及其在微分方程中的应用，数学机械化等领域的研究工作。已在SCI系统发表学术论文100余篇，发表论文已被SCI他引1000多次。主持完成国家自然科学基金3项，中国博士后基金1项，浙江省自然科学基金2项。参与完成国家自然科学基金和省、市自然科学基金多项。现参加国家自然科学基金重点项目一项，主持国家自然科学基金面上1项。