学术报告报告题目1：An insight into the q-difference two-dimensional Toda lattice equation, q-difference sine-Gordon equation and their integrability
报 告人1：李春霞教授(首都师范大学)
报告时间：2022年6月18日(星期六)上午9:30-10:30
报告地点：腾讯会议, 会议号：747-241-750
报告题目2：Higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation: Asymptotic analysis and emergence of rogue waves
报 告人2：许韬 教授(中国石油大学（北京））
报告时间：2022年6月18日(星期六) 上午10:30-11:30
报告地点：腾讯会议, 会议号：747-241-750
报告题目3：From the NLS to the full water waves
报 告人3：苏庆堂助理研究员(中国科学院)
报告时间：2022年 6月18日(星期六)下午15:30-16:30
报告地点：四号楼4131室
邀 请人：凌黎明教授
欢迎广大师生前往！
数学学院
2022年 6月17日
报告1摘要：In this talk, we first propose a generalized bilinear Bäcklund transformation and thus a generalized Lax pair for the bilinear q-difference two-dimensional Toda lattice (q-2DTL) equation. Next, starting from the known Darboux transformation for the noncommutative q-2DTL equation, we construct the existing Casoratian solutions to the bilinear q-2DTL equation and its bilinear Bäcklund transformation obtained by Hirota's bilinear method. And then, we successfully construct the binary Darboux transformation for the q-2DTL equation, based on which, Grammian solutions expressed in terms of quantum integrals are established for both the bilinear q-2DTL equation and its bilinear Bäcklund transformation. This reveals the profound connections between Darboux transformation and Hirota's bilinear method. In the end, by considering the 2-periodic reductions on the corresponding results of the q-2DTL equation, a q-difference sine-Gordon equation, a modified q-sG equation and their solutions are reported for the first time.
报告人简介1：李春霞, 首都师范大学数学科学学院教授, 博士生导师. 博士毕业于中国科学院数学院计算数学所, 研究方向为孤子理论与可积系统. 2005年-2007年在清华大学做博士后, 2007-2008年受英国皇家学会资助在英国格拉斯哥大学从事博士后研究工作。 先后作为国家公派留学人员和访问学者访问英国剑桥大学牛顿数学科学研究所、美国University of South Florida和College of Charleston. 先后主持国家自然科学基金面上项目2项、青年基金项目1项, 北京市自然科学基金面上项目2项等. 目前主要研究经典可积系统和非交换可积系统的构造和可积性质、可积系统与正交多项式、可积系统与矩阵模型及随机矩阵理论中的矩阵积分等不同数学领域的交叉. 部分研究工作发表在Journal of Nonlinear Science, Proceedings of the Royal Society A, Journal of Physics A和Inverse Problems等上。
报告2摘要：In this talk, we derive the determinant representation of higher-order algebraic soliton solutions of the Gerdjikov-Ivanov equation by using the Darboux transformation and some limit technique. Then, based on the asymptotic balance between different algebraic terms, we obtain the asymptotic expressions of algebraic soliton solutions with the order 2≤N≤4. It turns out that all the asymptotic solitons have the same amplitudes, most of them are located in the parabolic curves and thus have the varying velocities (except that one pair of asymptotic solitons are located in the straight lines for the odd-order cases), and they exhibit the elastic interactions of the attractive type. In addition, we reveal that the transient rogue waves are formed in the soliton-interaction region and the peak value is exactly N times the amplitude of individual soliton.
报告人简介2：许韬, 中国石油大学(北京)理学院数学系教授, 博士生导师. 先后于北京航空航天大学和北京邮电大学获得学士和博士学位, 曾受留学基金委资助访问过美国布法罗大学和加拿大麦克马斯特大学. 主要从事可积系统和非线性数学物理方程研究, 主持国家自然科学基金1项、北京市自然科学基金1项. 近年来, 在Physica D、Proceedings A、Physical Review E、Physics Letters A、Journal of Mathematical Physics等期刊发表第一、通讯作者论文40余篇, 累计SCI他引次数达1000余次。
报告3摘要：The 1d cubic focusing NLS is integrable and is extended studied, and has many interesting solitons. In this talk, I will discuss how to incorporate the NLS into the full water waves. In such a way, one can use the NLS solutions to construct approximate solutions to the water waves. In particular, I will discuss how to rigorously justify the Peregrine soliton from the 2d full water waves and the proof of the nonlinear modulational instability of the Stokes waves.
报告人简介3：苏庆堂, 博士毕业于美国密歇根大学, 师从女数学家邬似珏教授。2019年-2022年在南加州大学任助理教授(博士后), 现为中国科学院数学与系统科学研究院助理研究员， 研究方向为偏微分方程。