河南师范大学学报(自然科学版)

2021, v.49;No.221(06) 77-81

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导数非线性Schr?dinger方程的爆破解
Blow-up solutions for derivative nonlinear Schr?dinger equations

郑昊昊;李用声;
Zheng Haohao;Li Yongsheng;School of Mathematics, South China University of Technology;

摘要(Abstract):

研究下述导数非线性Schr9dinger方程的初边值问题:i?_t+α?_(xx)=iβ|?|~(2σ)?_x-g(|?|~2)?,σ≥1,x∈[a,b],其中α,β为实数,g(·)是实值函数.当α,β,?_0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 Schr9 dinger equations, i?_t+α?_(xx)=iβ|?|~(2σ)?_x-g( |?|~2) ?,σ≥1,x∈[a, b],where α, β are real, g(·) is a real function. Under the some appropriate conditions on α, β, ?_0 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(KeyWords): 导数非线性Schr?dinger方程;爆破解;修正的virial等式
derivative nonlinear Schr?dinger equation;blow-up solution;modified virial identity

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11571118;11971356)

作者(Author): 郑昊昊;李用声;
Zheng Haohao;Li Yongsheng;School of Mathematics, South China University of Technology;

Email:

DOI: 10.16366/j.cnki.1000-2367.2021.06.011

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