部分外场势垒中具双幂非线性项的非线性Schr?dinger方程驻波解的强不稳定性  

Strong Instability of the Standing Waves for the Double-power Nonlinear Schrdinger Equation with a Partial Confinement

作　　者：秦溢 黄娟 QIN Yi;HUANG Juan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan;Visual Computing and Virtual Reality Key Laboratory of Sichuan Province,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2024年第3期394-400,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12171343);四川省科技计划资助项目(2022JDTD0019和2022ZYD0009)。

摘　　要：研究一类在N维空间中具双幂非线性项的非线性Schr9dinger方程驻波解的强不稳定性.首先,利用Gagliardo-Nirengberg不等式、紧性引理和Brézis-Lieb引理得到驻波解的存在性.再借助不规则的Virial恒等式构造出与方程相关的发展不变流形.最后,通过对发展不变流形的研究获得驻波解的强不稳定性.In this paper,we study the strong instability of standing waves for double-power nonlinear Schrdinger equations with a partial confinement.Firstly,the existence of the ground states is obtained by Gagliardo-Nirengberg inequality,compactness lemma and Brézis-Lieb lemma.Secondly,by applying with irregular variance identity,invariant evolution flows related to the equation are constructed.Finally,we study the strong instability of solutions for the standing waves by investigating the invariant evolution flows.

关 键 词：部分势 驻波 强不稳定性 

分 类 号：O175.29[理学—数学]