Long time asymptotics for the focusing nonlinear Schrodinger equation in the solitonic region with the presence of high-order discrete spectrum
报告题目(Title)：Long time asymptotics for the focusing nonlinear Schrodinger equation in the solitonic region with the presence of high-order discrete spectrum
报告人(Speaker)：范恩贵 教授（复旦大学数学科学学院）
地点(Place)：后主楼 1223
时间(Time)：5月22日(周六)，9:30-10:30
邀请人(Inviter)：王灯山
报告摘要
In this paper, we study the initial value problem for focusing nonlinear Schrodinger (fNLS) equation with non-generic weighted Sobolev initial data that allows for the presence of high-order discrete spectrum. We obtain the asymptotic expansion of the solution of the fNLS equation in any fixed space-time cone. This result is a verification of the soliton resolution conjecture for the fNLS equation in the solitonic region with the presence of high-order discrete spectrum. The leading order term of this solution includes a high-order pole-soliton whose parameters are affected by soliton-soliton interactions through the cone and soliton-radiation interactions on continuous spectrum. The error term is up to O(t^{-3/4}) which comes from the corresponding Dbar equation.
主讲人简介
范恩贵，复旦大学数学科学学院教授、博士生导师，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；曾获教育部自然科学二等奖、上海市自然科学二等奖、谷超豪数学奖；主持国家自然科学基金、教育部博士点基金、上海曙光计划、上海曙光计划跟踪课题等多项研究课题。
