Global Solutions of Modified One-Dimensional Schr?dinger Equation

• 作者: Ting Zhang
• 来源期刊: 数学研究通讯
• 年，卷（期）: 2021,（3）
• 页码范围: 349-385
• 页数: 37页
• 语种: 英文
• DOI: 10.4208/cmr.2021-0015

摘要

In this paper,we consider the modified one-dimensional Schr?din-ger equation:(Dt-F(D))u=λ|u|2u,where F(ζ)is a second order constant coefficients classical elliptic symbol,and with smooth initial datum of size ε(＜＜)1.We prove that the solution is global-in-time,combining the vector fields method and a semiclassical analysis method introduced by Delort.Moreover,we get a one term asymptotic expansion for u when t →+∞.