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arXiv · 2601.03968

The uniqueness and concentration behavior of solutions for a nonlinear fractional Schr\"odinger system

Chungen Liu·Zhigao Zhang·Jiabin Zuo
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Abstract

The paper is concerned with a nonlinear system of two coupled fractional Schr\"odinger 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.

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Chungen Liu, Zhigao Zhang, Jiabin Zuo. 2026-01-07. The uniqueness and concentration behavior of solutions for a nonlinear fractional Schr\"odinger system. https://arxiv.org/abs/2601.03968

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