Three dimensional bright vortex soliton

Using the method of separation of variables, we developed a vector nonparaxial theory for the nonlinear wave equations in strong field approximation. We found that exact localized vortex soliton solution exists for the nonlinear 3D+1 vector wave equation and for 3D+1 vector nonlinear Schr\"{o}dinger equation. This method is applicable for angular functions, which satisfy additional conditions. It is shown that exact vortex solitary wave exists only for solution with eigenvalue of momentum L=1