Stokes surfaces of diffraction catastrophes with codimension three.

*(English)*Zbl 0706.65133The Stokes sets were introduced by *F. J. Wright* [J. Phys. A 13, 2913-2928 (1980; Zbl 0514.58009)] in recognition of the discovery of the phenomenon by Stokes and as a generalization of the so called Stokes line familiar in the asymptotics of special functions in the complex plane.

Wright calculated the Stokes sets of the cups singularity, for which $N=2$. The purpose of the article is to determine the Stokes sets for three of the canonical “diffraction catastrophes” that describe structurally stable wavefields in the short-wave limit. The authors have calculated explicitly and completely Stokes sets for all three of the stable singularities with $N=3:$ the swallowtail and the elliptic and hyperbolic umbilics.

Reviewer: S.V.Rogozin

##### MSC:

65Z05 | Applications of numerical analysis to physics |

37N99 | Applications of dynamical systems |

35Q60 | PDEs in connection with optics and electromagnetic theory |

78A45 | Diffraction, scattering (optics) |

33C10 | Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$ |

78A05 | Geometric optics |