  Using the method of separation of variables, we developed a vector
nonparaxial theory from the nonlinear wave equations in strong field
approximation of a Kerr media. Investigating three waves on different
frequencies, which satisfied the condition 2w3=w1+w2, we found that exact
localized vortex parametric soliton solutions existed for the set of four
nonlinear 3D+1vector wave equations. The solutions are obtained for a fixed
angle between the main frequencies and the signal waves A=60 deg. This method
is applicable for angular functions, which satisfy additional conditions. It is
shown that exact parametric vortex solitary waves exist for solution with
eigenrotation momentum L=1. The method is generalized for arbitrary number of
signal waves appearing symmetrically in pairs in respect to w3. The existence
of such type of vortex solitons, in the case of degenerate four-wave mixing is
discussed. As all of the waves are localized and have momentum L=1, they are
called optical mesons.
