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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03968 |
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| _version_ | 1866912807947075584 |
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| author | Liu, Chungen Zhang, Zhigao Zuo, Jiabin |
| author_facet | Liu, Chungen Zhang, Zhigao Zuo, Jiabin |
| contents | The paper is concerned with a nonlinear system of two coupled fractional Schrödinger equations with both attractive intraspecies and attractive interspecies interactions in $\mathbb{R}$. By analyzing an associated $L^2$-constrained minimization problem, the uniqueness of solutions to this system is proved via the implicit function theorem. Under a certain type of trapping potential, by establishing some delicate energy estimates, we present a detailed analysis on the concentration behavior of the solutions as the total strength of intraspecies and interspecies interactions tends to a critical value, where each component of the solutions blows up and concentrates at a flattest common minimum point of the associated trapping potentials. An optimal blow-up rate of solutions to the system is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03968 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The uniqueness and concentration behavior of solutions for a nonlinear fractional Schrödinger system Liu, Chungen Zhang, Zhigao Zuo, Jiabin Analysis of PDEs 35R11, 35J50, 35Q40 The paper is concerned with a nonlinear system of two coupled fractional Schrödinger equations with both attractive intraspecies and attractive interspecies interactions in $\mathbb{R}$. By analyzing an associated $L^2$-constrained minimization problem, the uniqueness of solutions to this system is proved via the implicit function theorem. Under a certain type of trapping potential, by establishing some delicate energy estimates, we present a detailed analysis on the concentration behavior of the solutions as the total strength of intraspecies and interspecies interactions tends to a critical value, where each component of the solutions blows up and concentrates at a flattest common minimum point of the associated trapping potentials. An optimal blow-up rate of solutions to the system is also given. |
| title | The uniqueness and concentration behavior of solutions for a nonlinear fractional Schrödinger system |
| topic | Analysis of PDEs 35R11, 35J50, 35Q40 |
| url | https://arxiv.org/abs/2601.03968 |