Abstract
We deal with the attractive Bose–Einstein condensates with sinusoidal potential in a circular region \(S:=\{x:0\le |x|\le \pi \}\subset {\mathbb {R}}^{2}\). The existence, non-existence and mass concentration behavior (i.e., blow-up) of constrained minimizers for the related Gross-Pitaevskii energy functional are analyzed. Once the blow-up behavior arises, we prove that the mass of positive minimizers must concentrate at center of the circular region, rather than the points of circumference.
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The authors are very grateful to Professor Yujin Guo for his fruitful discussions in the present paper.
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The research was supported by NSFC grant 11901500 and Nanhu Scholars Program for Young Scholars of XYNU.
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Zhu, X., Wang, C. Mass Concentration Behavior of Attractive Bose–Einstein Condensates with Sinusoidal Potential in a Circular Region. Mediterr. J. Math. 21, 12 (2024). https://doi.org/10.1007/s00009-023-02549-1
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DOI: https://doi.org/10.1007/s00009-023-02549-1