on the existence of non-radial normalized solutions for coupled fractional nonlinear schrödinger systems with potential

We investigate the existence of non-radial positive normalized solutions to coupled fractional nonlinear schr¨odinger 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 e 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.