Geodesic
Equivalence groupes of eikonal equation and classes of equivalent equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 4, pp. 3-42 
A. V. Borovskikh. Equivalence groupes of eikonal equation and classes of equivalent equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 4, pp. 3-42. http://geodesic.mathdoc.fr/item/VNGU_2006_6_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the papre the resuts describing the foliation of the family of eikonal equations onto classes of equivalence is presented. The technique of the group analysis is used: symmetry groups, equivalence groupes, for all family and for subfamilies, groups induced by the equivalence group on the manifolds of parameters, describing the classifying equations. To the extension of the group idees the notion of the cone of tangent equivalences is introduced, this notion is used for the analysis of the connection between the general and the partial equivalence groups.

[1] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[2] Sobolev S. L., “Volnovoe uravnenie dlya neodnorodnoi sredy”, Tr. Seismol. in-ta, 1930, no. 6, 1–57 | Zbl

[3] Gogoladze V. G., “Volnovoe uravnenie dlya neodnorodnykh i anizotropnykh sred”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 9 (1935), 107–166

[4] Babich V. M., Buldyrev V. S., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 | MR

[5] Kravtsov Yu. A., Orlov Yu. I., Geometricheskaya optika neodnorodnykh sred, Nauka, M., 1980 | MR

[6] Brekhovskikh L. M., Godin O. A., Akustika sloistykh sred, Nauka, M., 1989

[7] Borovskikh A. V., “Gruppovaya klassifikatsiya uravnenii eikonala dlya trekhmernoi neodnorodnoi sredy”, Mat. sb., 195:4 (2004), 23–64 | DOI | MR | Zbl

[8] Borovskikh A. V., “Dvumernoe uravnenie eikonala”, Sib. mat. zhurn., 47:5 (2006), 993–1018 | MR | Zbl

[9] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[10] Ovsyannikov L. V., “Programma PODMODELI. Gazovaya dinamika”, PMM, 58:4 (1994), 30–55 | MR | Zbl