On stability and instability of standing waves for the nonlinear Schrodinger equation with an inverse-square potential

被引：21

作者：

Bensouilah, Abdelwahab ^{[1
]}

Van Duong Dinh ^{[2
]}

Zhu, Shihui ^{[3
,4
]}

机构：

[1] Univ Lille 1, UFR Math, CNRS, Lab Paul Painleve,UMR 8524, F-59655 Villeneuve Dascq, France

[2] Univ Toulouse, CNRS, UMR5219, Inst Math Toulouse, F-31062 Toulouse 9, France

[3] Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 10期

基金：

中国国家自然科学基金;

关键词：

BLOW-UP SOLUTIONS; CRITICAL NLS; SCATTERING;

D O I：

10.1063/1.5038041

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the stability of standing waves for the focusing nonlinear Schrodinger equation with an inverse-square potential. Using the profile decomposition arguments, we show that in the L-2-subcritical case, i.e., 0 < alpha < 4/d, the sets of ground state standing waves are orbitally stable. In the L-2-critical case, i.e., alpha = 4/d, we show that ground state standing waves are strongly unstable by blow-up. Published by AIP Publishing.

引用

页数：18

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