Tanabé, Susumu 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]. Reviewer: Viorel Iftimie (Bucureşti) 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, \({}_pF_q\) Keywords:initial algebraic variety; Gauss-Manin systems PDFBibTeX XMLCite \textit{S. Tanabé}, Banach Cent. Publ. 50, 287--304 (1999; Zbl 0951.35074) Full Text: EuDML