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.
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页数：18
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