独特性
特征向量
格罗斯-皮塔耶夫斯基方程
玻色-爱因斯坦凝聚体
最大值和最小值
类型(生物学)
组分(热力学)
物理
非线性系统
规范(哲学)
数学物理
能量泛函
数学
应用数学
数学分析
量子力学
政治学
生物
法学
生态学
作者
Yujin Guo,Xiaoyu Zeng,Huan-Song Zhou
出处
期刊:Discrete and Continuous Dynamical Systems
[American Institute of Mathematical Sciences]
日期:2017-04-01
卷期号:37 (7): 3749-3786
被引量:16
摘要
The paper is concerned with a system of two coupled time-independent Gross-Pitaevskii equations in $\mathbb{R}^2$, which is used to model two-component Bose-Einstein condensates with both attractive intraspecies and attractive interspecies interactions. This system is essentially an eigenvalue problem of a stationary nonlinear Schr\"odinger system in $\mathbb{R}^2$, solutions of the problem are obtained by seeking minimizers of the associated variational functional with constrained mass (i.e. $L^2-$norm constaints). Under certain type of trapping potentials $V_i(x)$ ($i=1,2$), the existence, non-existence and uniqueness of this kind of solutions are studied. Moreover, by establishing some delicate energy estimates, we show that each component of the solutions blows up at the same point (i.e., one of the global minima of $V_i(x)$) when the total interaction strength of intraspecies and interspecies goes to a critical value. An optimal blowing up rate for the solutions of the system is also given.
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