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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
65Z05Applications of numerical analysis to physics
37N99Applications of dynamical systems
35Q60PDEs in connection with optics and electromagnetic theory
78A45Diffraction, scattering (optics)
33C10Bessel and Airy functions, cylinder functions, 0 F 1
78A05Geometric optics