An asymptotic expansion of the hyberbolic umbilic catastrophe integral (Q6116100)

The authors derive the asymptotic expansion of the hyperbolic umbilic catastrophe integral \(\psi^{(H)} (x, y, z) :=\int_{-\infty} ^{\infty}\int_{-\infty} ^{\infty} \exp(i (s^3 + t^3 + zst +yt + xs))ds dt\) for large \(|x|\) and bounded \(|y|\) and \(|z|\) values. The expansion is provided in terms of inverse powers of \(x\) and Airy functions. At arg \(x = \pi\), there is just a single Stokes ray. Also, the authors employ the modified saddle point method. Numerical investigations demonstrated in the approximations' accuracy and asymptotic character.