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The relationship between two different asymptotic techniques developed inorder to describe the propagation of waves beyond the standard geometricaloptics approximation, namely, the Wigner-Weyl kinetic formalism and the complexgeometrical optics method, is addressed. More specifically, a solution of thewave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained whichyields the same wavefield intensity as the complex geometrical optics method.Such a relationship is also discussed on the basis of the analytical solutionof the wave kinetic equation specific to Gaussian beams of electromagneticwaves propagating in a ``lens-like'' medium for which the complex geometricaloptics solution is already available.Comment: Extended version comprising two new section

The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method