摘要
本文考虑2维2次的规范不变的非线性薛定谔方程,研究它在H^(0,2)(R^(2))上的整体有界性.并且通过导出波包中测试函数的渐近方程得到了它的修正散射.这种使用波包测试函数的方法容许同时考虑问题在物理空间和频率空间的渐近性质.
In this paper,we consider the 2D quadratic gauge-invariant nonlinear Schrodinger equation.We set up its global bound in H^(0,2)(R^(2)).We also obtain its modified scattering by deriving an asymptotic equation for the test functions in the wave packets.This method allows us to consider the asymptotic properties of the problem both in the physical space and the frequency space.
作者
李俊峰
李想
LI Junfeng;LI Xiang(School of Mathematical Sciences,Dalian University of Technology,Dalian,Liaoning,116024,P.R.China;Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing,100875,P.R.China)
出处
《数学进展》
CSCD
北大核心
2021年第4期496-510,共15页
Advances in Mathematics（China）
基金
Supported by NSFC-DFG(No.11761131002)。
关键词
整体有界性
临界指数
修正散射
2次非线性薛定谔方程
global boundedness
critical index
modified scattering
quadratic nonlinear Schr?dinger eguation
