讲座题目：Multi-breather and high-order rogue waves for the nonlinear Schrdinger equation on the elliptic function background 主讲人：凌黎明 教授 主持人：陈勇 教授 开始时间：2020-08-25 15:00:00 结束时间：2020-08-25 17:00:00 讲座地址：腾讯会议(会议 ID：617 490 849 ) 主办单位：数学科学学院
报告人简介： 凌黎明，华南理工大学教授。长期从事非线性可积系统的研究，在可积系统“怪波”理论的发展中作出了一系列工作，率先同合作者给出高阶怪波解的Darboux 变换方法以及无穷阶怪波的分析理论。报告人在该方向上已经发表 40余篇 SCI 论文，其中 Duke Mathematical Journal， Physical Review E ，Physica D, Studies in Applied Mathematics, Nonlinearity 等杂志，合作出版怪波专著一部。已发表文章在 Google 学术搜索统计引用 1800 余次，H 指数 16，其中单篇最高引用 500 次，4篇入选ESI高被引论文。曾主持国家自然科学基金项目2项。 报告内容： In this talk, we construct the multi-breather solutions of the focusing nonlinear Schrödinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The dynamics of the breathers in the presence of various kinds of backgrounds such as dn, cn, and nontrivial phase-modulating elliptic solutions are presented, and their behaviors dependent on the effect of backgrounds are elucidated. We also determine the asymptotic behaviors for the multibreather solutions with different velocities in the limit t→±∞, where the solution in the neighborhood of each breather tends to the simple one-breather solution. Furthermore, we exactly solve the linearized NLSE using the squared eigenfunction and determine the unstable spectra for elliptic function background. By using them, the Akhmediev breathers arising from these modulational instabilities are plotted and their dynamics are revealed. Finally, we provide the rogue wave and higher order rogue wave solutions by taking the special limit of the breather solutions at branch points and the generalized Darboux transformation. The resulting dynamics of the rogue waves involves rich phenomena, depending on the choice of the background and possessing different velocities relative to the background. We also provide an example of the multiand higher order rogue wave solution. Joint with Bao-Feng Feng and Daisuke A. Takahashi. |
