60周年校庆系列讲座－－5月29日冯宝峰教授：Complex short pulse equation and its integrable discretization

　　主讲人：冯宝峰教授
　　地点：屏峰校区理A110
　　时间：2013年5月29日（周三）14:50—15:50
　　主办单位：理学院
　　联系电话：85290306
    
　　主讲人简介：
　　冯宝峰，美国得克萨斯泛美大学教授，在数学物理，特别是可积系统及其应用领域作出卓越的贡献。
    
　　讲座简介：
　　In the present talk, we propose a complex short pulse equation (CSPE) which may be more suitable for the description of ultra short pulse propagation in nonlinear optic fibers than the original short pulse equation. First, we derive the complex short pulse equation from a reduction of a multi-component generalization of the SPE and prove its multi-soliton solution in terms of pfaffians. We then analyze the one- and two-soliton solutions in detail, and show that the envelop soliton is of smooth, cuspon or loop type depending on the complex wave number of the pfffian solution.
　　In the second part of the talk, we construct integrable semi-discrete analogue of the complex short pulse equation by Hirota’s bilinear method and provide its multi-soliton solution. Finally, we show that this integrable discretization can be successfully used as a self-adaptive moving mesh method for the numerical simulation of the CSPE. The results of various numerical experiments including cuspon-loop envelop interaction are presented, showing a good agreement with exact solutions.
　　This is a joint work with Dr. Ohta at Kobe University and Dr. Maruno at the University of Texas-Pan American.