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- W3100508507 abstract "As a continuation of our prior article, we study new pattern formations of ground states $(u_1,u_2)$ for two-component Bose-Einstein condensates (BEC) with homogeneous trapping potentials in $mathbb {R}^2$, where the intraspecies interaction $(-a,-b)$ and the interspecies interaction $-beta$ are both attractive, i.e., $a$, $b$, and $beta$ are all positive. If $0<b<a^*:=|w|^2_2$ and $0<beta <a^*$ are fixed, where $w$ is the unique positive solution of $Delta w-w+w^3=0$ in $mathbb {R}^2$, the semi-trivial behavior of $(u_1,u_2)$ as $anearrow a^*$ is proved in the sense that $u_1$ concentrates at a unique point and while $u_2equiv 0$ in $mathbb {R}^2$. However, if $0<b<a^*$ and $a^*le beta <beta ^*=a^*+sqrt {(a^*-a)(a^*-b)}$, the refined spike profile and the uniqueness of $(u_1,u_2)$ as $anearrow a^*$ are analyzed, where $(u_1,u_2)$ must be unique, $u_1$ concentrates at a unique point, and meanwhile $u_2$ can either blow up or vanish, depending on how $beta$ approaches $a^*$." @default.
- W3100508507 created "2020-11-23" @default.
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- W3100508507 date "2019-02-14" @default.
- W3100508507 modified "2023-10-14" @default.
- W3100508507 title "Ground states of two-component attractive Bose-Einstein condensates II: Semi-trivial limit behavior" @default.
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- W3100508507 doi "https://doi.org/10.1090/tran/7540" @default.
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