题  目: A generalized Camassa-Holm equation and its peakon solutions

报告人: Dr. Zhijun Qiao，乔志军博士，美国德克萨斯大学数学系，终身教授

时  间：2015年6月15日（星期一）上午8:15

地  点：威廉希尔官网会议室

 

摘要：In this work, we study an integrable system with both quadratic and cubic nonlinearity. This model is kind of a cubic generalization of the Camassa-Holm (CH) equation. The equation is shown integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. In the case of no linear term, the peaked soliton (peakon) and multi-peakon solutions are presented. In particular, the two-peakon dynamical system is explicitly presented and their collisions are investigated in details. In some special case, the weak kink and kink-peakon interactional solutions are found. Significant difference from the CH equation is analyzed through a comparison. In the paper, we also study all possible smooth one-soliton solutions for the system.

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，洪堡基金研究员。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，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。