The uniqueness and concentration behavior of solutions for a nonlinear fractional Schrödinger system

2026/01/31 by Chungen Liu, Zhigao Zhang, Jiabin Zuo
Mathematics · #math.AP #msc:35R11 #msc:35J50 #msc:35Q40

paper · pdf

26 pages

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

The paper is concerned with a nonlinear system of two coupled fractional Schrödinger equations with both attractive intraspecies and attractive interspecies interactions in ℝ. By analyzing an associated L²-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.

Citations

• Fractional Gross-Pitaevskii equations in non-Gaussian attractive Bose-Einstein condensates
• Normalized ground states for the critical fractional NLS equation with a\n perturbation
• Normalized solutions for the fractional NLS with mass supercritical\n nonlinearity
• Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials
• Nonlocal Harnack inequalities for nonlocal heat equations
• The Brezis-Nirenberg result for the fractional Laplacian
• Uniqueness of radial solutions for the fractional Laplacian