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

文献类型：期刊论文

作者Guo, Yujin2; Wang, Zhi-Qiang3,4; Zeng, Xiaoyu1,5; Zhou, Huan-Song1,5
刊名NONLINEARITY
出版日期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
DOI10.1088/1361-6544/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
WOS记录号WOS:000424661900001
出版者IOP PUBLISHING LTD
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)
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.

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来源：武汉物理与数学研究所

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