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On geometry of fronts in wave propagations

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Tanabé,  Susumu
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4064/-50-1-287-304
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Citation

Tanabé, S. (1999). On geometry of fronts in wave propagations. In Geometry and topology of caustics—CAUSTICS '98 (pp. 287-304). Warszawa: Institute of Mathematics, Polish Academy of Sciences.


Cite as: https://hdl.handle.net/21.11116/0000-0004-7089-3
Abstract
We give a geometric description of (wave) fronts in wave propagation processes. The concrete form of the defining function of a wave front issuing from the initial algebraic variety is obtained with the aid of the Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagation on the plane, we get restrictions on the types of possible cusps that can appear on the wave front.