讲座题目：Integrablepeakon and cuspon equations

讲座人: 乔志军 教授

讲座时间：09:00

讲座日期：2015-6-6

地点：长安校区 文津楼三段612室

主办单位：英国正版365官方网站

讲座内容：

In my talk, I will introduce integrablepeakon and cuspon equations and present a basic approach how to get peakon solutions. Those equations include the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations with M/W-shape soutions. I take the CH case as a typical example to explain the details. My presentation is based on my previous work (Communications in Mathematical Physics 239, 309-341). I will show that the Camassa-Holm (CH) spectral problem yields two different integrable hierarchies of nonlinear evolution equations (NLEEs), one is of negative order CH hierachy while the other one is of positive order CH hierarchy. The two CH hierarchies possess the zero curvature representations through solving a key matrix equation. We see that the well-known CH equation is included in the negative order CH hierarchy while the Dym type equation is included in the positive order CH hierarchy. In particular, the CH equation, constrained to a symplecticsubmanifold in R^2N, has the parametric solutions. Moreover, solving the parametric representation of the solution on the symplecticsubmanifold gives a class of a new algebro-geometric solution of the CH equation. In the end of my talk, some open problems are also addressed for discussion.

讲座人简介：

乔志军，师从谷超豪院士和胡和生院士, 1997年毕业于复旦大学数学系，获博士学位。1997-2001任辽宁大学数学系教授。1999年获全国百篇优博论文。于1999-2001获洪堡基金资助赴德国卡塞尔综合大学交流学习。现为美国德克萨斯大学数学系终身教授，主管研究生项目，有30余位海外专家合作者, 已指导5位博士后及20余位研究生，组织超过20个国际会议及研讨会。主持完成10多个国家项目，出版著作2部，发表论文130余篇，其中包括著名国际杂志《数学物理学通讯》、《非线性科学》等。研究方向主要为：非线性偏微分方程、可积系统与非线性水波、KdV方程和孤立子理论、可积辛映射、R-矩阵理论、雷达图像处理和数学物理等问题。