题    目：Integrable two-component Camassa-Holm type systems with peakons, weak kink solutions, and their interactions

主讲人：乔志军 教授

单    位：美国德克萨斯大学

时    间：2025年1月8日 9:00

地    点：学院一楼报告厅

摘    要： In this talk, we present integrable two-component CH-type 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 reductions from two-component models and amazing solutions, such as nontraveling type of peakons, weak-kink-peakons, and rogue peakons. In particular, we first time propose weak-kink solutions, rogue peakon solutions, and weak-kink-peakon interaction solutions [1, 2, 3]. Those results are joint work with my collaborator Dr. Baoqiang Xia and Dr. Ruguang Zhou.

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

简    介：乔志军博士，美国德克萨斯大学UTRGV讲席教授。1986-1989年获得郑州大学硕士学位，师从曹策问教授。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,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, 2023年被授予Fulbright项目国际专家。主持完成国家级和国际级项目20余项。在国际一流期刊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 之一。