报告题目：Recent Developments on Integrable Peakon Systems

报告人：乔志军  教授

报告时间：2021年10月29日(周五)上午8:30—10:30

报告地点：腾讯会议，ID: 823 912 110

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. 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 peakon equation is extended to the FORQ/MCH and other higher order peakon models with peakon and weak-kink solutions. In the end of my talk, some open problems are also addressed for discussion.

报告人简介: 乔志军，美国德克萨斯大学首席教授。1997年获得复旦大学博士学位,师从谷超豪院士和胡和生院士。主要从事非线性偏微分方程,可积系统与非线性尖孤波,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等领域的研究。1999年获全国首届百篇优秀博士论文, 1999-2001年在德国Kassel大学任Humboldt学者。主持完成国家级和国际级项目20余项。在国际顶级刊物Communications in Mathematical Physics、IEEE Transaction on Geoscience and Remote Sensing (TGRS)等发表学术论文150多篇,出版著作2部。现任国际权威刊物Studies in Applied Mathematics编委和Journal of Nonlinear Mathematical Physics主编。

数学与统计学院

                   2021年10月22日