Title: Integrable Peakon Models and Beyond
Speaker: Zhijun Qiao
Institution: University of Texas Rio Grande Valley
Date & Time: June 22, 2024, 16:00–18:00
Location: Zoom ID: 904 645 6677, Password: 2024
This talk introduces recently developed integrable peakon models and presents a fundamental approach to constructing peakon solutions for integrable equations. Specifically, the CH (Camassa-Holm) peakon equation is extended to quadratic and cubic peakon models in the b-family (e.g., FORQ, MOCH, Novikov Equations) with peakon and weak-kink solutions. We also discuss a new CH-type equation—the fifth-order CH equation—and introduce novel solutions called pseudo-peakon solutions and their interactions. Part of this work is joint with Dr. BQ Xia and Dr. E Reyes. Open problems will be proposed for discussion at the end.
Prof. Zhijun Qiao received his PhD in Mathematics from Fudan University in 1997, supervised by Academicians Chaohao Gu and Hesheng Hu. He completed postdoctoral research at Peking University (1997–1999) and was awarded the National Hundred Excellent Doctoral Theses in 1999. A Humboldt Fellow (1999–2001), he is currently a Chair Professor in the Department of Mathematics at the University of Texas Rio Grande Valley. His research focuses on nonlinear partial differential equations, integrable systems, nonlinear peakons, KdV equations, soliton theory, integrable symplectic maps, R-matrix theory, radar image processing, and inverse problems in mathematical physics. He has authored 2 books and published over 180 papers in renowned journals such as
Communications in Mathematical Physics and
Journal of Nonlinear Science. As a principal investigator, he has completed more than 20 national and international research projects, organized over 20 international conferences and workshops, and serves as an editorial board member for
Studies in Applied Mathematics and Editor-in-Chief of
Journal of Nonlinear Mathematical Physics.
