四川大学学报（自然科学版）2023，Vol.60Issue(2)：49-56,8.DOI:10.19907/j.0490-6756.2023.021006
非线性Schrödinger方程长时间稳定性的一个估计
An estimation of the long time stability of the nonlinear Schrodinger equation
摘要
Abstract
In this paper,the stability of the nonlinear Schr?dinger equation iψ=-△ψ+F(| ψ|2)ψ,x ∈ T is considered on the one-dimensional torus,where T:=R/2πZ,F:R→R is analytic,F(0)=0 and F'(0)≠0.Under the regularity index s fulfilling that 1/2＜s＜1,we give an estimate for the long time stability of small amplitude solutions with initial data of size ε,where ε is positive and sufficiently small.More precisely,we prove that the modulus of the Fourier coefficients of solutions is approximately con-stant for the time order ε-(4+2/9s).关键词
非线性Schrödinger方程/小振幅解/长时间稳定性Key words
Nonlinear Schrödinger equation/Small amplitude solutions/Long time stability(2010 MSC 37K45)分类
数理科学引用本文复制引用
李海阔..非线性Schrödinger方程长时间稳定性的一个估计[J].四川大学学报（自然科学版）,2023,60(2):49-56,8.基金项目
国家自然科学基金(11971299) （11971299）
