- Zhijun Qiao
- President's Endowed Professor
- University of Texas Rio Grande Valley
- Date: Oct. 28, Wednesday, 2026
- Time: 14:00-14:50
- Host: Yanzhao Cao
- Room: STEM Ag 2111
- Abstract: In this talk, I will introduce some integrable scalar models which possess peaked solitons (peakons), including the well-known Camassa-Holm (CH), the Degasperis-Procesi (DP), and other new peakon equations developed in recent years. I will take the CH case as a typical example to explain the details and show that the Camassa-Holm (CH) spectral problem yields two different integrable hierarchies of nonlinear evolution equations. In particular, the CH peakon equation is able to be extended to the DP, the b-family, the FORQ, the Novikov, the modified CH (MoCH), and other higher order models with peakons or pseudo-peakons. Some open problems will also be addressed for discussion in the end. Some work is joint with Dr. Baoqiang Xia and Dr. Enrique Reyes.