Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials

doi:10.1088/1361-6544/aa99a8

	Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials
	Guo, Yujin 2; Wang, Zhi-Qiang 3,4; Zeng, Xiaoyu 1,5; Zhou, Huan-Song 1,5
刊名	NONLINEARITY
	2018-03-01
卷号	31 期号:3 页码:957-979
关键词	Ground States Constrained Variational Problem Gross-pitaevskii Equation Multi-well Potential
ISSN号	0951-7715
DOI	10.1088/1361-6544/aa99a8
文献子类	Article
英文摘要	We are interested in the attractive Gross-Pitaevskii (GP) equation in R-2, where the external potential V(x) vanishes on m disjoint bounded domains Omega(i) subset of R-2 (i = 1, 2, . . . , m) and V(x) -> infinity as vertical bar x vertical bar -> infinity, that is, the union of these Omega(i) is the bottom of the potential well. By establishing some delicate estimates on the associated energy functional of the GP equation, we prove that when the interaction strength a approaches some critical value a, the ground states concentrate and blow up at the center of the incircle of some Omega(j) with the largest inradius. Moreover, under some further conditions on V(x), we show that the ground states of the GP equations are unique and radially symmetric at least for almost every a is an element of (0, a).
WOS关键词	NONLINEAR SCHRODINGER-EQUATIONS ; BOSE-EINSTEIN CONDENSATION ; SYMMETRY-BREAKING ; POSITIVE SOLUTIONS ; STANDING WAVES ; GAS ; UNIQUENESS ; BIFURCATION ; EXISTENCE ; R(N)
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000424661900001
资助机构	NSFC(11471331 ; NSFC(11471331 ; MOST(2017YFA0304500) ; MOST(2017YFA0304500) ; 11771324 ; 11771324 ; 11501555 ; 11501555 ; 11671394) ; 11671394) ; NSFC(11471331 ; NSFC(11471331 ; MOST(2017YFA0304500) ; MOST(2017YFA0304500) ; 11771324 ; 11771324 ; 11501555 ; 11501555 ; 11671394) ; 11671394) ; NSFC(11471331 ; NSFC(11471331 ; MOST(2017YFA0304500) ; MOST(2017YFA0304500) ; 11771324 ; 11771324 ; 11501555 ; 11501555 ; 11671394) ; 11671394) ; NSFC(11471331 ; NSFC(11471331 ; MOST(2017YFA0304500) ; MOST(2017YFA0304500) ; 11771324 ; 11771324 ; 11501555 ; 11501555 ; 11671394) ; 11671394)
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/12854]
专题	中国科学院武汉物理与数学研究所
通讯作者	Zhou, Huan-Song
作者单位	1.Wuhan Univ Technol, Ctr Math Sci, Wuhan 430070, Hubei, Peoples R China 2.Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Hubei, Peoples R China 3.Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China 4.Utah State Univ, Dept Math, Logan, UT 84322 USA 5.Wuhan Univ Technol, Dept Math, Wuhan 430070, Hubei, Peoples R China
推荐引用方式 GB/T 7714	Guo, Yujin,Wang, Zhi-Qiang,Zeng, Xiaoyu,et al. Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials[J]. NONLINEARITY,2018,31(3):957-979.
APA	Guo, Yujin,Wang, Zhi-Qiang,Zeng, Xiaoyu,&Zhou, Huan-Song.(2018).Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials.NONLINEARITY,31(3),957-979.
MLA	Guo, Yujin,et al."Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials".NONLINEARITY 31.3(2018):957-979.