系列学术报告：*

1. Title: Hierarchy of Integrable Equations and Lax Pair

Abstract: In this talk, we discuss hierarchy of integrable equations and Lax pair.  I will present a two-component short pulse system produced through a negative integrable flow associated with the WKI hierarchy. The Lax representation will be given for the whole hierarchy. Particularly, some eigenvalue problems are provided for investigating the spectrum distribution. The multi-soliton solutions for the two short pulse system investigated, in particular, one-, two-, three-loop soliton, and breather soliton solutions are discussed in details with interesting dynamical interactions and shown through figures. This is joint work with Qiaoyi Hu and Qilao Zha.

 时间：2020年12月16日上午9:00-11:00

腾讯会议ID：723 871 786 （会议密码：123456）

2. Title: Negative order KDV hierarchy

Abstract: In this talk, we first show the classical procedure about how to get the KdV soliton and other classical solitons. Then we study the negative KdV flows and related peakon, cuspon, and compacton solutions. We also present some important applications in water waves propagation. Further investigation will be needed.

  时间：2020年12月17日上午10:00-11:30

腾讯会议ID：258 756 759

3. Title: Degasperis Procesi (DP) equation and 3 by 3 Lax pair

Abstract: In the b-family system, only the CH (b=2) and the DP (b=3) equations is found integrable so far. In this talk, we will display some significant difference between the CH and DP. The DP equation can be extended to the whole integrable hierarchy associated with a 3 by 3 Lax pair through inverse of recursion operator. Some exact solutions are addressed for the positive and negative order members in the hierarchy.

 时间：2020年12月18日上午10:00-11:30

腾讯会议ID：533 789 829

报告人：乔志军教授

       美国得克萨斯大学

个人简历：乔志军，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。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、Journal of Nonlinear Science、Journal of Differential Equations、IEEE Transaction on Geoscience and Remote Sensing (TGRS)等发表学术论文100多篇,出版著作2部。现任国际一流刊物Studies in Applied Mathematics编委。