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Stokes surfaces of diffraction catastrophes with codimension three. (English) Zbl 0706.65133

The 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