[1]李玉林,黄 娟*,周 凡.具有平方反比势的非齐次非线性Schrdinger方程驻波的强不稳定性[J].四川师范大学学报(自然科学版),2020,43(01):27-32.[doi:10.3969/j.issn.1001-8395.2020.01.003]
 LI Yulin,HUANG Juan,ZHOU Fan.Strong Instability of the Standing Waves for the Inhomogeneous Nonlinear Schrdinger Equation with Inverse-square Potential[J].Journal of SichuanNormal University,2020,43(01):27-32.[doi:10.3969/j.issn.1001-8395.2020.01.003]
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具有平方反比势的非齐次非线性Schrödinger方程驻波的强不稳定性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年01期
页码:
27-32
栏目:
基础理论
出版日期:
2019-12-04

文章信息/Info

Title:
Strong Instability of the Standing Waves for the Inhomogeneous Nonlinear Schrödinger Equation with Inverse-square Potential
文章编号:
1001-8395(2020)01-0027-06
作者:
李玉林 黄 娟* 周 凡
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
LI Yulin HUANG Juan ZHOU Fan
College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
平方反比势 驻波 强不稳定性
Keywords:
inverse-square potential blow-up strong instability
分类号:
O175.29
DOI:
10.3969/j.issn.1001-8395.2020.01.003
文献标志码:
A
摘要:
讨论一类在三维空间中具有平方反比势的非齐次非线性Schrödinger方程.首先构造一个典型的交叉约束变分问题及几个强制约束变分问题,得到相应的发展不变流形.通过对这些变分问题及发展不变流形的研究,得到爆破解存在的充分条件及其驻波的强不稳定性.
Abstract:
In this paper, we study the focusing cubic inhomogeneous nonlinear Schrödinger equation with inverse-square potential in three dimensions. By constructing a typical cross-constrained variational problem and several constraint variational problems, we get the corresponding invariant evolution flows. Analyzing these variational problems and these invariant evolution flows, the sufficient conditions of the blow-up solutions and the strong instability of the standing waves are obtained for the Cauchy problem.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2018-03-23 接受日期:2018-08-28 基金项目:国家自然科学基金(11401409)和四川省科技厅应用基础研究项目(2018JY0486) *通信作者简介:黄 娟(1982—),女,副教授,主要从事数学物理和偏微分方程的研究,E-mail:hjmath@163.com
更新日期/Last Update: 2019-12-04