Geodesic
The novel class of exact solutions of the two-dimensional eikonal equation when the velocity in a~medium depends on one spatial coordinate
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 3, pp. 259-271.

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The method to obtain solutions of the two-dimensional eikonal equation has been developed for the case when the velocity of wave propagation in a medium depends only on one spatial coordinate. We present several examples, where the initial problem is transformed to one or several ordinary differential equations using the substitution of the solution into a suitable general form. The dynamics of the wave propagation for each solution obtained is illustrated. 
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E. D. Moskalensky. The novel class of exact solutions of the two-dimensional eikonal equation when the velocity in a~medium depends on one spatial coordinate. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 3, pp. 259-271. http://geodesic.mathdoc.fr/item/SJVM_2018_21_3_a2/

[1] Borovskikh A. V., “Dvumernoe uravnenie eikonala”, Sib. mat. zhurnal., 47:5 (2006), 993–1018 | MR | Zbl

[2] Marchuk An. G., Chubarov L. B., Shokin Yu. I., Chislennoe modelirovanie voln tsunami, Nauka, Novosibirsk, 1983

[3] Marchuk An. G., “Vychislenie vysoty tsunami, rasprostranyayuscheisya nad naklonnym dnom, v luchevom priblizhenii”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 18:4 (2015), 377–388 | MR | Zbl

[4] Marchuk An. G., “Otsenka vysoty tsunami, rasprostranyayuscheisya nad parabolicheskim dnom v luchevom priblizhenii”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 20:1 (2017), 23–35 | MR | Zbl

[5] Filippov A. T., Mnogolikii soliton, Nauka, M., 1986 | MR

[6] Moskalensky E. D., “On detecting a wavefront described by 2D eikonal equation, when the velocity in the medium depends on one spatial variable”, Num. Anal. and Appl., 3:1 (2010), 52–58 | DOI