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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.27455 |
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| _version_ | 1866910179715448832 |
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| author | Hu, Wenhao Li, Benniao Long, Wei Wang, Chunhua |
| author_facet | Hu, Wenhao Li, Benniao Long, Wei Wang, Chunhua |
| contents | We consider the following two-component coupled nonlinear Schrödinger (CNLS) system: \[ \begin{cases} -Δu +(P(x) + λ) u=μ_1 u^3+βu v^2, & \text{in } \mathbb{R}^N,\\ -Δv +(Q(x) + λ) v =μ_2 v^3+βvu^2, & \text{in } \mathbb{R}^N \end{cases} \] with the mass constraint $\int_{\mathbb{R}^N} (u^2+v^2)\,dx = ρ^2$ for $N=2,3$, where $ρ>0$ is a parameter. By employing the Lyapunov-Schmidt reduction and local Pohozaev identities, we establish the existence and local uniqueness of normalized multi-peak solutions: the result holds for sufficiently small $ρ$ when $N=3$, and for $ρ$ approaching a critical threshold when $N=2$. The main difficulty lies in that the mass constraint involves interactions among all concentration points, while a more refined characterization of such normalized solutions further requires sharp order estimates. In this work, we have discovered some new phenomena that differ from those of solutions without mass constraint and single-peak solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_27455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness of Normalized Multi-peak Solutions for Coupled Nonlinear Schrödinger Systems Hu, Wenhao Li, Benniao Long, Wei Wang, Chunhua Analysis of PDEs 35J10, 35J47, 35J60 We consider the following two-component coupled nonlinear Schrödinger (CNLS) system: \[ \begin{cases} -Δu +(P(x) + λ) u=μ_1 u^3+βu v^2, & \text{in } \mathbb{R}^N,\\ -Δv +(Q(x) + λ) v =μ_2 v^3+βvu^2, & \text{in } \mathbb{R}^N \end{cases} \] with the mass constraint $\int_{\mathbb{R}^N} (u^2+v^2)\,dx = ρ^2$ for $N=2,3$, where $ρ>0$ is a parameter. By employing the Lyapunov-Schmidt reduction and local Pohozaev identities, we establish the existence and local uniqueness of normalized multi-peak solutions: the result holds for sufficiently small $ρ$ when $N=3$, and for $ρ$ approaching a critical threshold when $N=2$. The main difficulty lies in that the mass constraint involves interactions among all concentration points, while a more refined characterization of such normalized solutions further requires sharp order estimates. In this work, we have discovered some new phenomena that differ from those of solutions without mass constraint and single-peak solutions. |
| title | Existence and Uniqueness of Normalized Multi-peak Solutions for Coupled Nonlinear Schrödinger Systems |
| topic | Analysis of PDEs 35J10, 35J47, 35J60 |
| url | https://arxiv.org/abs/2604.27455 |