Report Title： An Introduction to Soliton Models in Mathematical Physics
Speaker: Qiao Zhijun
Affiliation: University of Texas
Time: December 15, 2025, 16:00–18:00
Venue: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
Solitons are remarkable phenomena in nature, exhibiting complex interactions governed by fundamental principles of mathematics and physics. This introductory talk aims to present, in an accessible manner, the basic models of solitary water waves and their significance. We begin by discussing the fundamental characteristics of solitary waves, emphasizing that they can retain their stable shape and constant propagation speed even after interacting with other waves. These unique properties make solitons a highly attractive subject in both theoretical and applied research.
We then review the development of soliton models, starting with the Korteweg–de Vries (KdV) equation, which provides a foundational understanding of one-dimensional soliton behavior in shallow water. The KdV equation elegantly captures the balance between nonlinearity and dispersion, a key mechanism underlying the persistence of solitary wave structures. In addition, we introduce more advanced models, such as the Burgers equation and the Camassa–Holm equation, which extend the study of solitary waves to more complex shallow water environments. These models help reveal the rich dynamical behavior of wave propagation and interactions under different physical settings. Finally, the talk will briefly introduce our current interdisciplinary Ph.D. program in mathematics and statistics, as well as funding opportunities for international students, including Graduate Teaching Assistantships (GTA) and Graduate Research Assistantships (GRA).
Biography of the Speaker:
Dr. Qiao Zhijun is a Chair Professor at the University of Texas Rio Grande Valley (UTRGV), USA. He received his master’s degree from Zhengzhou University (1986–1989) under the supervision of Professor Cao Cewen, and his Ph.D. from Fudan University in 1997 under the supervision of Academicians Gu Chaohao and Hu Hesheng. His research interests include nonlinear partial differential equations, integrable systems and nonlinear peakons, the KdV equation and soliton theory, integrable symplectic maps, R-matrix theory, image processing, and inverse problems in mathematical physics.
In 1999, he received the National Award for 100 Excellent Doctoral Dissertations in China, and from 1999 to 2001 he was a Humboldt Research Fellow at the University of Kassel, Germany. He received the Distinguished Research Award from the University of Texas in 2013, was appointed Chair Professor in 2016, and was named a Fulbright Specialist in 2023. He has led more than 20 national and international research projects, published over 150 papers in leading journals such as Communications in Mathematical Physics and IEEE Transactions on Geoscience and Remote Sensing (TGRS), and authored two books. He currently serves on the editorial board of Studies in Applied Mathematics and as one of the Editors-in-Chief of the Journal of Nonlinear Mathematical Physics.
