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

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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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     author = {E. D. Moskalenskii},
     title = {On one approach to solving the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {361--370},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a3/}
}
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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/