报告题目：Scalar peakon model and beyond

报告时间：2021年12月6日 10:00-12:00

报告地点：腾讯会议：270918258

报告人： 乔志军教授

美国德克萨斯大学讲席教授。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。2013年获德克萨斯大学杰出研究奖，2016年被授予德克萨斯大学讲席教授。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。

报告摘要：In this talk, I will introduce some integrable scalar models which possess peaked solitons (peakons), including the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations developed in recent years. I will take the CH case as a typical example to explain the details and show that the Camassa-Holm (CH) spectral problem yields two different integrable hierarchies of nonlinear evolution equations. In particular, the CH peakon equation is able to be extended to the DP, the b-family, the FORQ, the Novikov, the modified CH (MOCH), and other higher order models with peakons or pseudo-peakons. Some open problems will also be addressed for discussion in the end.