Propagation of rotating parabolic cylindrical beams in nonlocal nonlinear medium

I introduce a class of rotating parabolic cylindrical beams in nonlocal nonlinear media. The rotating speed keeps fixed in the case of strong nonlocality and increases with the nonlocality being weak. For the strong nonlocal case, the analytical solutions of the modified Snyder Mitchell model agree well with the numerical simulations of the nonlocal nonlinear Schrödinger equation. By simulating the propagation of the rotating parabolic cylindrical beams in liquid crystal and nonlinear thermal media numerically, I demonstrate that there exists the rotating parabolic cylindrical cosine Gaussian quasi-soliton state.