 In other words, the first term of γ"ab" decomposition corresponds to "H" = 0; higher terms are obtained by powers decomposition of matrix "H" whose components are considered small.The independent components of matrix "H" are written as σ and φ so that
Substituting in and leaving only terms linear by "H", one derives for σ and φ
If one tries to find a solution to these equations as [[Fourier series]] by the "z" coordinate, then for the series coefficients, as functions of ξ, one obtains Bessel equations.The major asymptotic terms of the solution at large ξ are

Coefficients "A" and "B" are arbitrary complex functions of coordinates "x", "y" and satisfy the necessary conditions for real σ and φ; the base frequency ω is an arbitrary real function of "x", "y".