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Zbl 0706.65133
Berry, M.V.; Howls, C.J.
Stokes surfaces of diffraction catastrophes with codimension three. (English)
[J] Nonlinearity 3, No.2, 281-291 (1990). ISSN 0951-7715; ISSN 1361-6544/e

The Stokes sets were introduced by {\it 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. \par 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.
[S.V.Rogozin]

MSC 2000:: *65Z05 Applications to physics
37N99 Applications of dynamical systems
35Q60 PDE of electromagnetic theory and optics
78A45 Diffraction, scattering (optics)
33C10 Cylinder functions, etc.
78A05 Geometric optics

Keywords: Stokes sets; Stokes line; asymptotics of special functions; cups singularity; diffraction catastrophes; wavefields; short-wave limit; swallowtail; elliptic and hyperbolic umbilics

Citations: Zbl 0514.58009

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