【大学频道】西北大学物理学院呈献 | 德克萨斯大学冯宝峰教授

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图 | 冯宝峰教授

题   目：The complex short pulse equation and its integrable discretization

报告人：冯宝峰

单   位：德克萨斯大学

时   间：2019-04-19

地   点：西北大学

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报告摘要

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.

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个人简介

冯宝峰，教授，毕业于清华大学，后留学日本获得名古屋大学硕士和京都大学博士学位，现任德克萨斯大学数学与统计学院终身教授。主要从事非线性科学方面的研究，特别是可积系统和孤立子理论方面的研究，迄今在国际著名期刊上发表论文70余篇，被引用超千次。先后组织了5次国际会议，担任在美国乔治亚大学每两年举办的非线性波国际会议，海峡两岸可积系统会议，中日可积系统会议以及中国孤立子与可积系统会议组委会成员。因其独立提出的非线性格子以及非线性光学超短脉冲波的数学模型，先后获得美国国防部以及美国自然科学基金三十多万美元的研究资助。近年来经常受邀回国访问，分别通过清华大学和上海交通大学获得中国自然科学基金海外及港澳学者合作基金。

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