Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 2, pp. 201-209
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E. D. Moskalenskii. Finding exact solutions to the two-dimensional eikonal equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 2, pp. 201-209. http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a6/
@article{SJVM_2009_12_2_a6,
author = {E. D. Moskalenskii},
title = {Finding exact solutions to the two-dimensional eikonal equation},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {201--209},
year = {2009},
volume = {12},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a6/}
}
TY - JOUR
AU - E. D. Moskalenskii
TI - Finding exact solutions to the two-dimensional eikonal equation
JO - Sibirskij žurnal vyčislitelʹnoj matematiki
PY - 2009
SP - 201
EP - 209
VL - 12
IS - 2
UR - http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a6/
LA - ru
ID - SJVM_2009_12_2_a6
ER -
%0 Journal Article
%A E. D. Moskalenskii
%T Finding exact solutions to the two-dimensional eikonal equation
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2009
%P 201-209
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2009_12_2_a6/
%G ru
%F SJVM_2009_12_2_a6
In this paper, the two-dimensional eikonal equation $f_x^2+f_y^2=\phi^2$, where $\phi=\frac1{v}$, and $v(x,y)$ is a wavespropagation velocity, is discussed. This non-linear equation is reduced to a quasilinear equation for a new dependent variable $u$. For some kinds of the functions $\phi$, solutions to the quasilinear equations are found. This means that it is possible to solve the original equation for such $\phi$. This paper also offers an approach to finding a new solution based on a known one.
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