On checking through some of the equations, I noticed a rather fundamental error in eq (10). Using the quoted asymptotic expansions for the Airy functions, I get an extra factor on the right-hand side. Since y 1 and y 2 are both large, this dominates the curly bracket term which the authors obviously got in expanding the term
Therefore, G(X) is corrected (to within a first order) by replacing it byIt would appear that the authors overlooked that the phase factor in the asymptotic form of the Airy function is a stronger function of t than the amplitude factor.