报告人：Baofeng Feng 教授

Department of Mathematics，University of Texas-Pan American

报告题目：Bilinearizations and integrable discretizations for a class of nonlinear wave equations

报告时间：2013年7月2日  星期二  下午4：30-5：30
  
报告地点：管理科研楼1218教室

报告摘要:
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 first 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 clarified. 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.

主办单位: 中国科学技术大学数学科学学院          中科院吴文俊数学重点实验室

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