Integrable Peakon Systems

Abstract

In this talk, we will introduce integrable peakon models in nonlinear sciences and present a basic approach how to get the peakon models and peakon solutions. We will see that the well-known Camassa-Holm (CH) equation is a very special reduction from the Navier-Stokes-\alpha model. In particular, the CH peakon equation is extended to the b-family quadratic and cubic peakon models with peakon and weak-kink solutions. We will also present new type of peakon solutions we recently found, called rogue peakons provided with a non-traveling wave. Some nonlinear models are taken to illustrate the rogue peakon solutions. In the end of my talk, some open problems are also addressed for discussion.

Biography

Dr. Zhijun Qiao is a President’s Endowed Chair Professor of Mathematics at the University of Texas Rio Grande Valley, USA. He earned his M.S. from Zhengzhou University and his Ph.D. in Mathematics from Fudan University in 1997. He received China’s National 100 Excellent Doctoral Dissertation Award in 1999 and was a Humboldt Research Fellow at the University of Kassel, Germany. His research focuses on nonlinear partial differential equations, integrable systems, soliton and peakon theory, image processing, and inverse problems in mathematical physics.

Dr. Qiao has led more than 20 research projects and published academic books and over 150 research papers including those top-level journals such as CMP etc., making substantial contributions to integrable nonlinear wave models. His honors include the University of Texas Distinguished Research Award in 2013 and selection as a Fulbright Specialist in 2023. He is an editor of Studies in Applied Mathematics and an Editor-in-Chief of the Journal of Nonlinear Mathematical Physics.