Title: From Discrete Integrable System to Continuous Integrable System
Time：     10:30-12:30, July3 Wednesday,2019
Location:   Room 202, Mathematical Building
Lecturer：Professor Baofeng Feng,Department of Mathematics, University of Texas-Pan, American

Abstract:
In this talk, I will give a review on recent development of integrable system, especially the discrete inegrable system. It is known that the tau-functions play a crucial role in both the continuous and discrete integrable sytems. We will start with a type of Gam determinant solution and show it satisfies the Hirota-Miwa equation, or the discrete Kadomtsev-Petviashvili (KP) equation. By introducing Schur polynomial, and Miwa transformation, we will derive the KP hierarchy, whose reductions give rise to the Korteweg-de Vries (KdV) equation and Boussinesq equation. Then we will show by simple transformations, the discrete KP equation can be transformed into discrete modified KP equation and the discrete KP-Toda lattice equation, which in turn lead to the modified KP and KP-Toda hierarchy, whose reductions give the modified KdV equation and Sine-Gordon equation, respectively.

Introduction of Lectuer:
Professor Bao Feng graduated from Tsinghua University with a bachelor's degree in physics and mathematics, and then received a doctorate from Kyoto University. He is now a tenured professor of utrgv School of mathematics and statistics at the University of Texas. Dr. Feng has made great achievements in the field of applied and computational mathematics. His research interests include nonlinear waves and their applications in hydrodynamics and nonlinear optics, continuous and discrete integrable systems, and numerical solutions of PDE. Professor Feng has published more than 70 academic papers in international well-known journals, and has received 6 project grants from the National Science Foundation of the United States, the overseas and Hong Kong Macao scholars cooperative research fund of the National Natural Science Foundation of China, the U.S. Department of defense and the Army Research Bureau. In 2007 and 2012, Dr. Feng was awarded the title of research fellow of Japan Society for academic revitalization. He visited Tokyo University, Kyoto University, Waseda University, etc., and organized four international conferences and more than 30 international conference topics.