理学院数理讲坛（2014年第二十三讲）
报 告 人：冯宝峰教授，美国德克萨斯(泛美）大学数学系
报告题目：Complex short pulse and coupled complex short pulse equations
报告时间：6月3日下午3:00
报告地点: 阳明学院303室
报告摘要：
In this talk, a complex short pulse equation (CSP) and a coupled complex
short equation (CCSP) are proposed to describe ultra-short pulse propagation
in optical bers. Firstly, starting from Maxwell equation, we derive the CSP
and CCSP equations by using multi scale perturbation method. By nding the
Lax pair and in nite number of conservation laws, we show that the CSP equation is always integrable but the CCSP equation is only integrable under one particular case. Furthermore, we nd their multi-soliton solutions in terms of
pfaffians by virtue of Hirota's bilinear method. One- and two-soliton solutions
are investigated in details, showing favorable properties in modeling ulta-short
pulses with a few optical cycles. Especially, same as the coupled nonlinear
Schrodinger equation, interactions between two solitons are basically inelastic
with energy redistribution. If time permits, we will show how to construct the
integrable dicretizations of the CSP and CCSP equations and apply them as
self-adaptive moving mesh methods for numerical simulations.
欢迎有兴趣老师和研究生参加。