Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation

In this paper, we investigate the dynamics and stability of multi -peak solitons from the coupled nonlinear Schr & ouml;dinger equation with the fractional dimension based on L & eacute;vy random flights. By implementing linear stability analysis and direct simulations, we demonstrate regions where the single and multi -peak modes are stable. Analysis of perturbed coupled solitons confirms the stability of higher -order modes compared to lower -order modes under the same configurations. The stability diagrams show that the force coupling, L & eacute;vy index, power, and the nonlinear intensity significantly influence the stability of high -order modes. Our findings indicate that stability is favored in self -defocusing systems with high L & eacute;vy indices under weak coupling conditions, with higher -order states exhibiting smaller stability regions.