Geodesic
On one approach to solving the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 361-370 
E. D. Moskalenskii. On one approach to solving the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 361-370. http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a3/
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     title = {On one approach to solving the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper offers a new approach to finding a solution to the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$ with a variable velocity of the waves propagation $V(x,y,z)(\phi=1/V)$. It is based on a certain change of a dependent variable and reduction of the equation to a system of three quasilinear equations. It is shown that for certain cases of the function $V(x,y,z)$, exact solutions to this equation can be found with the help of the approach proposed.

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