Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 1, pp. 67-73
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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},
pages = {67--73},
year = {2010},
volume = {13},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a5/}
}
TY - JOUR
AU - E. D. Moskalensky
TI - On detecting a wavefront described by 2D eikonal equation, when velocity in a medium depends on one spatial variable
JO - Sibirskij žurnal vyčislitelʹnoj matematiki
PY - 2010
SP - 67
EP - 73
VL - 13
IS - 1
UR - http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a5/
LA - ru
ID - SJVM_2010_13_1_a5
ER -
%0 Journal Article
%A E. D. Moskalensky
%T On detecting a wavefront described by 2D eikonal equation, when velocity in a medium depends on one spatial variable
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2010
%P 67-73
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2010_13_1_a5/
%G ru
%F SJVM_2010_13_1_a5
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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[2] Zaitsev V. F., Polyanin A. D., Spravochnik po differentsialnym uravneniyam s chastnymi proizvodnymi pervogo poryadka, Fiziko-matematicheskaya literatura, M., 2003 | Zbl
