Numerical variational approach for vortex solitons in nonlinear Schrödinger equation

We study the generation and dynamics of asymmetric vortex solitons in nonlocal media described with an additional parameter that models the degree of azimuthal asymmetry. The main properties of vortex solitons are investigated analytically and numerically, in the numerical case we use a recently introduced numerical variational method based on the Rayleigh- Ritz optimization principle, we find that nonlocality and the degree of asymmetry can stabilize the proposed vortex solitons. We corroborate the results reported by using spectral techniques.