On the existence of non-radial normalized solutions for coupled fractional nonlinear Schrödinger systems with potential

Document Type : Research Article

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Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain

Abstract

We investigate the existence of non-radial positive normalized solutions to coupled fractional nonlinear Schrödinger systems characterized by competing nonlinearities and subject to multiple \( L^2 \) norm constraints. Considering a local minimization strategy within specially constructed symmetric function spaces and applying the concentration-compactness principle, we demonstrate the existence of multiple non-radial solutions that exhibit symmetry breaking relative to the radial symmetry of the external potential. Additionally, we conduct an asymptotic analysis as the semiclassical parameter \( \varepsilon \) approaches zero, revealing that the solutions localize around multiple distinct points where the potential attains its maximum values. These concentration points are arranged according to the symmetry imposed by a finite group of orthogonal transformations, leading to the formation of multi-bump profiles.

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Journal of Mathematical Modeling
Volume 13, Issue 2
May 2025
Pages 357-373

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