导数非线性Schr dinger方程的爆破解  

Blow-up solutions for derivative nonlinear Schr dinger equations

作　　者：郑昊昊 李用声 Zheng Haohao;Li Yongsheng(School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学数学学院,广州510640

出　　处：《河南师范大学学报（自然科学版）》2021年第6期77-81,共5页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11571118,11971356)。

摘　　要：研究下述导数非线性Schrodinger方程的初边值问题:iφ_(t)+αφ_(xx)=iβ|φ|^(2σ)φx-g(|φ|^(2))φ,σ1,x∈[a,b],其中α,β为实数,g(·)是实值函数.当α,β,φ0及g(s)满足一定条件时,利用守恒律和修正的virial等式,证明了爆破解的存在性.最后,得到了爆破解的渐近行为等一些性质.In this paper,we study the blow-up solutions to the following initial boundary value problem of the derivative nonlinear Schrodinger equations,iφ_(t)+αφ_(xx)=iβ|φ|^(2σ)φx-g(|φ|^(2))φ,σ1,x∈[a,b],whereα,βare real,g(·)is a real function.Under the some appropriate conditions onα,β,φ0 and g(s),we show the existence of the blow-up solutions by conservation laws and modified virial identity.Finally,we investigate asymptotic behavior and other properties of blow-up solutions.

关 键 词：导数非线性Schr dinger方程 爆破解 修正的virial等式 

分 类 号：O175.23[理学—数学]