报告题目 (Title)：Long time asymptotics for the focusing Fokas-Lenells equation in the solitonic region of space-time
报告人 (Speaker)： 范恩贵 教授（复旦大学）
报告时间 (Time)：2021年11月4日(周四) 15:00
报告地点 (Place)：线上腾讯会议 569 259 291
邀请人(Inviter)：夏铁成
报告摘要：We study the long time asymptotic behavior of the focusing Fokas-Lenells (FL) equation with generic initial data in a Sobolev space that support bright soliton solutions. The FL equation is an integrable generalization of Schrodinger equation, and also linked to the derivative Schrodinger model, but it exhibits several different characteristics from theirs. The Lax pair of the FL equation involves an additional spectral singularity at $k=0$, and four stationary phase points will appear during asymptotic analysis. These need a more detailed necessary description to obtain long time asymptotic of the focusing FL equation. Based on the Riemann-Hilbert problem for initial value problem of the focusing FL equation, we show that inside any fixed time-spatial cone, the long time asymptotic behavior of the solution for the focusing FL equation can be characterized with an N-soliton on discrete spectrum and leading order term O(|t|^{-1/2}) on continuous spectrum up to an residual error order O(|t|^{-3/4}).