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Integrable systems with weak kink, and kink-peakon interactional solutions

2018/06/05 14:29  点击:[]

报告人: Zhijun (George) Qiao(德州大学)

 

 : 20186月6  16:30--17:30

 

 

 : 理科楼LA106

 

 :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:乔志军现任美国德克萨斯大学数学学院首席教授 President’s Endowed Professor).乔教授于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,卡塞尔大学,数学系,洪堡学者,现有40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。现已出版著作2部,发表论文160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20多个国家项目。组织超过20个国际会议、研讨会。

 

学院联系人: 穆春来

 

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