Circle-like concentrated solutions for two-component Bose-Einstein condensates
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915818345857024 |
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| author | Guo, Qidong Hua, Qiaoqiao Tian, Chongyang |
| author_facet | Guo, Qidong Hua, Qiaoqiao Tian, Chongyang |
| contents | We investigate the normalized solutions of the following two-component Bose-Einstein condensates (BEC) system
\begin{equation}\left\{ \begin{split}
-Δu + (λ+P(x))u &= αu^3 +βuv^2, && \text{in } \mathbb{R}^2,\\-Δv + (λ+Q(x))v &= γv^3 +βu^2 v, && \text{in } \mathbb{R}^2, \end{split} \right.\end{equation}
with $L^2$-constraint $$\int_{\mathbb{R}^2}(u^2+v^2)\,dx = 1.$$ For any $α>0$, $γ> 0$ and $\ β\in (-\sqrt{αγ},0)\cup(0,\min \{α,γ\})\cup \left(\max \{α,γ\} , + \infty\right)$, we establish the existence of synchronized solutions concentrating on high-dimensional subsets of $\mathbb{R}^2$ by employing a finite-dimensional reduction method combined with some local Pohozaev identities. More precisely, we construct vector radial solutions that concentrate on circles when $ \frac{α+ γ- 2β}{αγ- β^2}$ tends to zero. Our results fill the blank in the system for high-dimensional concentrated normalized solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Circle-like concentrated solutions for two-component Bose-Einstein condensates Guo, Qidong Hua, Qiaoqiao Tian, Chongyang Analysis of PDEs We investigate the normalized solutions of the following two-component Bose-Einstein condensates (BEC) system \begin{equation}\left\{ \begin{split} -Δu + (λ+P(x))u &= αu^3 +βuv^2, && \text{in } \mathbb{R}^2,\\-Δv + (λ+Q(x))v &= γv^3 +βu^2 v, && \text{in } \mathbb{R}^2, \end{split} \right.\end{equation} with $L^2$-constraint $$\int_{\mathbb{R}^2}(u^2+v^2)\,dx = 1.$$ For any $α>0$, $γ> 0$ and $\ β\in (-\sqrt{αγ},0)\cup(0,\min \{α,γ\})\cup \left(\max \{α,γ\} , + \infty\right)$, we establish the existence of synchronized solutions concentrating on high-dimensional subsets of $\mathbb{R}^2$ by employing a finite-dimensional reduction method combined with some local Pohozaev identities. More precisely, we construct vector radial solutions that concentrate on circles when $ \frac{α+ γ- 2β}{αγ- β^2}$ tends to zero. Our results fill the blank in the system for high-dimensional concentrated normalized solutions. |
| title | Circle-like concentrated solutions for two-component Bose-Einstein condensates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.22672 |