Geodesic
On finding exact solutions of the two-dimensional eikonal equation when the front of the wave propagating in a~medium is a~circle
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 363-372.

Voir la notice de l'article provenant de la source Math-Net.Ru

Wave propagation in a two-dimensional medium is considered in the case when the front of the wave is a circle with the center $(a(t),0)$ and radius $r(t)$. A question is posed: what is the distribution of velocity in the medium? Common characteristics and examples of such media are given. 
@article{SJVM_2014_17_4_a4,
     author = {E. D. Moskalensky},
     title = {On finding exact solutions of the two-dimensional eikonal equation when the front of the wave propagating in a~medium is a~circle},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {363--372},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a4/}
}
TY  - JOUR
AU  - E. D. Moskalensky
TI  - On finding exact solutions of the two-dimensional eikonal equation when the front of the wave propagating in a~medium is a~circle
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2014
SP  - 363
EP  - 372
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a4/
LA  - ru
ID  - SJVM_2014_17_4_a4
ER  - 
%0 Journal Article
%A E. D. Moskalensky
%T On finding exact solutions of the two-dimensional eikonal equation when the front of the wave propagating in a~medium is a~circle
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2014
%P 363-372
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a4/
%G ru
%F SJVM_2014_17_4_a4
E. D. Moskalensky. On finding exact solutions of the two-dimensional eikonal equation when the front of the wave propagating in a~medium is a~circle. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 363-372. http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a4/

[1] Gurvich I. I., Boganik G. N., Seismicheskaya razvedka, Nedra, M., 1980

[2] Savelov A. A., Ploskie krivye. Sistematika, svoistva, primeneniya, Librokom, M., 2010

[3] Moskalenskii E. D., “O nakhozhdenii tochnykh reshenii dvumernogo uravneniya eikonala”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 12:2 (2009), 201–209

[4] Entsiklopediya elementarnoi matematiki. Kniga 4. Geometriya, Gosudarstvennoe izdatelstvo fiziko-matematicheskoi literatury, M., 1963