报告时间：2023年10月27日 14：00开始
报 告 人：张晓恩（山东科技大学 教授）
报告地点：包玉书9号楼305
报告题目：large-order asymptotics of the nonlinear Schrodinger equation
报告摘要：As we know, when two solitons admit the same velocity, they will form a breather in the vanishing background. If the corresponding spectrum of the Lax operator forms a high-order spectrum, the high-order breathers will be generated. In this work, we study the large-order asymptotics for this kind of breathers in the limit that the order is proportional to the variables x and t. We first formulate a Riemann-Hilbert problem of this breather via the Darboux transformation. When the order is large, the space-time plane is partitioned into five distinct regions. Using the Deift-Zhou nonlinear steepest descent method, we give the leading order terms for the five regions. Compared with the large-order asymptotics of solitons with a single spectral parameter, we first find a novel genus-three asymptotic region, which uncovers that the maximal genus of the asymptotic region is connected with the number of spectral parameters. All results of the asymptotic analysis are verified by the numerical method.
报告人简介：张晓恩，山东科技大学精英计划A类人才，学术教授。近年来主持国家自然科学青年基金项目一项，博士后面上项目一项，广州市基础与应用基础研究项目一项。主要从事可积系统方面的研究，发表SCI学术论文10多篇，其中ESI高被引论文4篇。
