Singularities of the propagation of shot waves on the plane
Sbornik. Mathematics, Tome 186 (1995) no. 11, pp. 1581-1597 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The subject of this paper is the geometric optics of linear shot waves on the plane. We describe the transformation fronts and scattering of rays when the light hypersurface has conic singularities. They appear if the waves propagate in a non-homogeneous anisotropic medium subject to the hyperbolic variational principle.
@article{SM_1995_186_11_a1,
     author = {I. A. Bogaevsky},
     title = {Singularities of the~propagation of shot waves on the~plane},
     journal = {Sbornik. Mathematics},
     pages = {1581--1597},
     year = {1995},
     volume = {186},
     number = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_11_a1/}
}
TY  - JOUR
AU  - I. A. Bogaevsky
TI  - Singularities of the propagation of shot waves on the plane
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 1581
EP  - 1597
VL  - 186
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_11_a1/
LA  - en
ID  - SM_1995_186_11_a1
ER  - 
%0 Journal Article
%A I. A. Bogaevsky
%T Singularities of the propagation of shot waves on the plane
%J Sbornik. Mathematics
%D 1995
%P 1581-1597
%V 186
%N 11
%U http://geodesic.mathdoc.fr/item/SM_1995_186_11_a1/
%G en
%F SM_1995_186_11_a1
I. A. Bogaevsky. Singularities of the propagation of shot waves on the plane. Sbornik. Mathematics, Tome 186 (1995) no. 11, pp. 1581-1597. http://geodesic.mathdoc.fr/item/SM_1995_186_11_a1/

[1] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. 8. Elektrodinamika sploshnykh sred, Nauka, M., 1992 | MR

[2] Arnold V. I., Singularities of caustics and wave fronts, Math. Appl. Soviet Ser., 62, Kluwer Acad. Publ., Dordrecht, 1990 | MR | Zbl

[3] Arnold V. I., “O poverkhnostyakh, opredelyaemykh giperbolicheskimi uravneniyami”, Matem. zametki, 44:1 (1988), 3–18 | MR

[4] Arnold V. I., “On the interior scattering of waves, defined by hyperbolic variational principles”, J. Geom. Phys., 5:3 (1988), 305–315 | DOI | MR | Zbl

[5] Khesin B. A., “Singularities of light hypersurfaces and structure of hyperbolicity sets for systems of partial differential equations”, Adv. Soviet Math., 1, AMS, 105–118 | MR | Zbl

[6] Arnold V. I., “Wave front evolution and equivariant Morse lemma”, Comm. Pure Appl. Math., 29:6 (1976), 557–582 | DOI | MR | Zbl

[7] Arnold V. I., Teoriya katastrof, Nauka, M., 1990 | MR

[8] Bogaevskii I. A., “Perestroiki frontov v evolyutsionnykh semeistvakh”, Tr. MIAN, 209, Nauka, M., 1995, 65–83 | MR | Zbl