报告题目：Integrability and Stability of Solitons to Nonlinear Dispersive Equations
报告时间地点：2024.11.22 8:00-8:40 机械楼B502
报告人：屈长征 国家杰青（宁波大学）
报告摘要：A typical property for integrable systems is the existence of solitons. Various methods have been applied to study stability of solitons of integrable systems. In the study of stability of solitons, integrability properties of integrable systems play key roles in study of stability of solitons. In this talk, we shall present a survey on the issue how the integrabilities be used in proving stability of solitons and other kinds of solutions. Some open questions related to this talk will be addressed.
报告题目：Lax pair and bilinear form of k-constrained differential-difference Kadomtsev- Petviashvili hierarchy
报告时间地点：2024.11.22 8:40-9:20 机械楼B502
报告人：陈奎 副研究员（之江实验室）
报告摘要：In this talk, we introduce the k-constrained differential-difference Kadomtsev-Petviashvili hierarchy, where the special case of k=1 is corresponding to the squared wavefunctions symmetry. The Ragnisco-Tu hierarchy is derived as taking k=1, and a semi-discrete analogue of Yajima-Oikawa hierarchy is produced as taking k=2. The Lax equation and bilinear identities of the k-constrained differential-difference Kadomtsev-Petviashvili hierarchy are constructed.
报告题目：CKP和modified CKP的一些研究进展
报告时间地点：2024.11.22 9:20-10:00 机械楼B502
报告人：程纪鹏 博导 (中国矿业大学)
报告摘要：CKP和modified CKP方程族是与C型无限维李代数对应的KP和modified KP方程族的一类重要约化。B型KP方程族与KP方程族的tau函数很类似，但是C型KP可积方程族的tau函数非常特殊，与KP和BKP方程族有很大的不同。本报告中主要介绍C型可积系统tau函数的玻色子构造，以及相应tau函数的构造等问题。
报告人简介：程纪鹏，中国矿业大学数学学院教授，博导， 江苏高校“青蓝工程”优秀青年骨干教师. 研究方向：数学物理、可积系统，目前主要研究KP及其相关可积系统，在Adv Math、IMRN、Lett Math Phys、J Math Phys、J Geom Phys、Sci China Math等国内外重要期刊发表科研论文60余篇. 主持在研国家自然科学基金面上项目一项。
报告题目：Dispersive Revival and fractalization Phenomena for Dispersive Evolution Equations
报告时间地点：2024.11.22 10:10-10:50 机械楼B502
报告人：康静 博导 (西北大学)
报告摘要：In this talk, we investigate the revival phenomena for the dispersive evolution equations. Firstly, we study the dispersive quantization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. Next, we present and analyze a novel manifestation of the revival phenomenon for bidirectional dispersive evolution equations, in the context of the beam equation. We give an analytic description of this phenomena, and present illustrative numerical simulations.
报告人简介：康静，西北大学数学学院教授、博导。主要研究方向为非线性可积系统。具体的研究课题包括：对称和李群在微分方程中的应用、非线性可积系统可积性及孤立波解、Liouville相关性理论及其应用。主持四项国家自然科学基金项目，一项陕西省自然科学基金杰出青年项目，入选“2017年度陕西省高校青年杰出人才支持计划”。
报告题目：On dynamics of solitary waves solutions for the generalized Camassa-Holm equation and related topics
报告时间地点：2024.11.22 10:50-11:30 机械楼B502
报告人：刘小川 国家优青 (西安交通大学)
报告摘要：The following generalized Camassa-Holm (CH) equation ut uxxt+2 ux+(p+1)(p+2) 2 upux = p(p 1) 2 up 2u3 x+2pup 1uxuxx+upuxxx with p Z+ appears originally in a paper by Hakkaev and Kirchev (Comm. PDE, 2005) as a special case of the family of CH-type equations: ut for a(u) = 2 u+ p+2 uxxt + a(u)x = 1 2 b(u)u2 x + b(u)uxx x 2 up+1 and b(u) = up. Later, Anco et al in (DCDEA, 2015) derived it in terms of one Hamiltonian structure of the classical CH equation. This higher-order equation admits smooth solitary wave solutions when = 0 and peaked solitary wave solutions c1/pe x ct (c > 0) if = 0. In this talk, I will report our recent results on the dynamical behavior of these solitary wave solutions and related results.
