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On geometry of fronts in wave propagations. (English) Zbl 0951.35074

Janeczko, Stanisław (ed.) et al., Geometry and topology of caustics - CAUSTICS ’98. Proceedings of the Banach Center symposium, Warsaw, Poland, June 15-27, 1998. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 50, 287-304 (1999).
Author’s abstract: We give a geometric description of (wave) fronts in wave propagation processes. The concrete form of the defining function of the wave front issued from the initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
For the entire collection see [Zbl 0931.00034].

MSC:

35L25 Higher-order hyperbolic equations
35A18 Wave front sets in context of PDEs
33C75 Elliptic integrals as hypergeometric functions
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
78A05 Geometric optics
33C20 Generalized hypergeometric series, \({}_pF_q\)
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