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学术报告
学术报告
美国德克萨斯大学数学系乔志军教授报告通知
发布人:系统管理员??威尼斯官方网站:2015-06-30?? 浏览次数:616

应数学系蒋卫华教授邀请,美国德克萨斯大学数学系乔志军教授报告将于近日访问我校理学院数学系,并进行讲学活动,欢迎感兴趣的师生参加!

 

报告题目:Integrable peakon and cuspon equations

报告时间:201572日下午1600--17:00

报告地点:格物楼503

 

报告摘要:In my talk, I will introduce integrable peakon 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 solutions. 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 hierarchy 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 symplectic submanifold in $R^2N$, has the parametric solutions. Moreover, solving the parametric representation of the solution on the symplectic submanifold 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.

  

报告人简介:乔志军于1997年获得复旦大学数学系博士学位,从师谷超豪院士和胡和生院士。1999年获得百篇优秀博士毕业论文。1997-2001任辽宁大学数学系教授。1999-2001,德国,卡塞尔综合大学,数学系,洪堡基金获得者。现任教于美国德克萨斯大学数学系,终身教授。主管研究生项目,现有30多位海外专家合作者已经指导5位博士后及超过20位研究生。研究方向是非线性偏微分方程,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的反问题。现已出版著作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。现作为项目负责人已经完成10多个个国家项目。组织超过20个国际会议、研讨会。
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