Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials
Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials
复制标题
具有多阱势的有吸引力的 Gross-Pitaevskii 方程的基态性质
DOI：
10.1088/1361-6544/aa99a8
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发表时间：
2018
期刊：
影响因子：
1.7
通讯作者：
H.-S. Zhou
中科院分区：
文献类型：
--
作者：
Yujin Guo;Z.-Q. Wang;X. Y. Zeng;H.-S. Zhou
我们感兴趣的是$R^2$中有吸引力的Gross-Pitaevskii(GP)方程，其中外势在不相交的有界域$\Omega_i\subset\R^2\(i=1，2，cdots，m)$andas上为零，即它们的并是势井的底部。通过对GP方程的能量泛函作一些精细的估计，我们证明了当相互作用强度接近某一临界值时，基态在内径最大的内圆的中心处集中并破裂。此外，在进一步的条件下，我们证明了GP方程的基态至少是唯一的，并且几乎每一次都是径向对称的。
We are interested in the attractive Gross-Pitaevskii (GP) equation in $\R^2$, where the external potentialvanishes ondisjoint bounded domains $\Omega_i\subset \R^2\ (i=1,2,\cdots,m)$ andas, that is, the union of theseis the bottom of the potential well. By making some delicate estimates on the energy functional of the GP equation, we prove that when the interaction strengthapproaches some critical valuethe ground states concentrate and blow up at the center of the incircle of somewhich has the largest inradius. Moreover, under some further conditions onwe show that the ground states of GP equations are unique and radially symmetric at leat for almost every.