主讲人：Prof. Baofeng Feng （Department of Mathematics, University of Texas-Pan American）

时  间：6月18日（周二）16：00-17：00

地  点：威尼斯欢乐娱人城1099北二区教学楼 130 教室

摘  要：Abstract: Recently, much attention has been paid to a class of nonlinear wave equations, which include the Camassa-Holm equation, the Degasperis-Procesi equation and their short-wave limits (the Hunter-Saxton and the reduced Ostrovsky equations), the short pulse and coupled short equations etc. These equations share some common features: (1) they are connected to some well-known integrable systems such as two-dimensional Toda-lattice via hodograph (reciprocal) transformations; (2) they admit bizarre solutions such as loop, cupon, peakon, or breather solutions. In the present talk, we will report our recent work on integrable discretizations for this class of soliton equations. By Hirota's bilinear method and appropriate discrete Hodograph transformation, we have successfully constructed integrable discretizations for most of these soliton equations, as well as their multi-soliton solutions. In the rst part of the talk, we will show the bilinear equations and multi-soliton solutions for some of this type of equations including two-component Camassa-Holm equation and its short wave limit. There relation with Camassa-Holm equation and Hunter-Saxton equation is also clari ed. In the second part, we will show how integrable discretizations can be constructed, and how can be used for the numerical simulation as a novel numerical method: self-adaptive moving mesh method.This is a joint work with Dr. Kenichi Maruno, Dr. Yasuhiro Ohta at Kobe University of Japan.