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

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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 L2 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 ε 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

Articles in Press, Corrected Proof
Available Online from 01 January 2025

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