Transformation of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation by means of Lévy-index management

The structure and stability of multipole and vortex solitons in the nonlocal nonlinear fractional Schrödinger equation with a gradually decreasing Lévy index, α, are numerically studied. It is found that the solitons adiabatically compress with the decrease of Lévy index, and new species of stable ones are produced by means of this technique. It is known that, under the action of the normal diffraction (α = 2), the nonlocal cubic self-trapping can support, at most, quadrupole solitons and vortex ones with winding number m = 2 as stable modes in the one- and two-dimensional space, respectively. In contrast to that, we find that the application of the Lévy index management (the gradual decrease of α) leads to the formation of stable five-poles and sextupoles in one-dimensional, and vortices with m = 3 in two-dimensional. Weak dissipation does not essentially affect the observed results. • The propagation of multipole and vortex solitons in NNFSE with a gradually decreasing Lévy index is studied. • The solitons adiabatically compress with the decrease of LI, and new species of stable ones are produced. • The profile, width and amplitude of beam all can be controlled by parameters of Lévy index. • The gradual decrease of α leads to the formation of stable five-poles and sextupoles in 1D, and vortices with m = 3 in 2D.