Local uniqueness and refined spike profiles of ground states for two-dimensional attractive Bose-Einstein condensates
Journal
SIAM Journal on Mathematical Analysis
Journal Volume
49
Journal Issue
5
Pages
3671-3715
Date Issued
2017
Author(s)
Abstract
We consider ground states of two-dimensional Bose-Einstein condensates in a trap with attractive interactions, which can be described equivalently by positive minimizers of the L2-critical constraint Gross-Pitaevskii energy functional. It is known that ground states exist if and only if a < a∗ := w22 , where a denotes the interaction strength and w is the unique positive solution of Δw - w + w3 = 0 in R2. In this paper, we prove the local uniqueness and refined spike profiles of ground states as a % a→, provided that the trapping potential h(x) is homogeneous and H(y) = RR2 h(x + y)w2(x)dx admits a unique and nondegenerate critical point.
SDGs
Type
journal article