Integrable two-component systems with peakons, weak kink solutions and their interactions
数学专题报告
报告题目(Title):Integrable two-component systems with peakons, weak kink solutions and their interactions
报告人(Speaker):乔志军(美国德克萨斯大学讲席教授)
地点(Place):后主楼1223;腾讯会议:685-654-5612
时间(Time):3月13日(周三),上午10:00-11:00
邀请人(Inviter):王灯山
报告摘要
In this talk, we present integrable two-component models with peakon and weak kink solutions. The two-component model is proven integrable through its Lax pair and infinitely many conservation laws. Moreover, we investigate the interaction of multi-peakons and interplaying of weak-kink with peakons for two-component models. We will also discuss about reductions from two-component models and discuss some very interesting solutions, such as nontraveling type of peakons, new type of N-peakon solutions, N-weak-kink solutions, weak hat-shape soliton solutions, periodic-peakon solutions, and rational peakon solutions. In particular, we first time propose N-weak-kink solutions, rational peakon solutions, and weak-kink-peakon interaction solutions [1, 2, 3]. Those results are joint work with my collaborator Dr. Baoqiang Xia.
References
[1] On integrable peakon systems with weak kink and kink-peakon interactional solutions, Frontiers of Mathematics in China 8(2013), 1185.
[2] A synthetical two-component model with peakon solutions, Studies in Applied Mathematics, 135(2015), 248
[3] A new two-component integrable system with peakon solutions. Proc. R. Soc. A, 471(2015), 20140750
主讲人简介
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年在德国任Humboldt学者。主持完成国家级和国际级项目20余项。在国际权威刊物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。已指导研究生和博士后数十名,现任国际著名刊物Studies in Applied Mathematics编委和Journal of Nonlinear Mathematical Physics主编之一。