Geodesic
On detecting a wavefront described by 2D eikonal equation, when velocity in a medium depends on one spatial variable
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 67-73 
E. D. Moskalensky. On detecting a wavefront described by 2D eikonal equation, when velocity in a medium depends on one spatial variable. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 67-73. http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a5/
@article{SJVM_2010_13_1_a5,
     author = {E. D. Moskalensky},
     title = {On detecting a~wavefront described by {2D} eikonal equation, when velocity in a~medium depends on one spatial variable},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a 2D eikonal equation $f_x^2+f_y^2=(ky+b)^{2\alpha}$ is considered. If its solution is found, then the relation $f(x,y)=C$ determines the location of a wavefront. However, finding such solutions is still an open question. In this paper, we propose to directly find a curve in the parametric form, corresponding to the wavefront, without solving the equation as it is.

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