学术报告
报告题目：Long time asymptotics for the defocusing mKdV equation with finite density initial data
报告人：范恩贵，复旦大学教授，博士生导师
报告时间：2021年8月25日10:00-11:00
腾讯会议：会议 ID：706 411 862
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We investigate the long time asymptotics for the Cauchy problem of the defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data in different solitonic regions. Based on the spectral analysis of the Lax pair, we express the solution of the mKdV equation in terms of an Riemann-Hilbert problem. In our previous article, we have obtained long time asymptotics and soliton solutions for the mKdV equation in the solitonic region \xi\in (-6;-2) with \xi = x/t. In this talk, we calculate the asymptotic expansion of the solution q(x; t) for the solitonic region \xi<-6. For \xi < -6, there exist four stationary phase points on jump contour, and the asymptotic approximations can be characterized with an N-soliton on discrete spectrums and a leading order term O(t^{-1/2}) on continuous spectrum up to a residual error order O(t^{-3/4}). For \xi > -2, the leading term of asymptotic expansion is described by the soliton solution and the error order O(t^{-1}) comes from a Dbar-problem.
专家简介：范恩贵，复旦大学数学科学学院教授、博士生导师、上海市“曙光学者”。曾获教育部自然科学二等奖、上海市自然科学二等奖、复旦大学谷超豪数学奖。1999年于大连理工大学获博士学位并进入复旦大学博士后流动站工作，师从谷超豪院士。曾应邀访问美国密苏里大学、密歇根州立大学、日本京都大学等。主要研究方向是孤立子理论、可积系统、Riemann-Hilbert问题、正交多项式和随机矩阵理论。近年来，连续两届为国家“973”课题成员并主持国家自然科学基金、上海“曙光计划”等多项研究课题，在国外重要刊物上发表论文100余篇，所发表论文被SCI刊源他引3000余次。