  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
