Geodesic
Equivalence of systems of two-dimensional shallow water equations over horizontal and sloping bottoms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 62-64 
A. V. Aksenov. Equivalence of systems of two-dimensional shallow water equations over horizontal and sloping bottoms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 62-64. http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a9/
@article{VMUMM_2023_6_a9,
     author = {A. V. Aksenov},
     title = {Equivalence of systems of two-dimensional shallow water equations over horizontal and sloping bottoms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {62--64},
     year = {2023},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a9/}
}
TY  - JOUR
AU  - A. V. Aksenov
TI  - Equivalence of systems of two-dimensional shallow water equations over horizontal and sloping bottoms
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 62
EP  - 64
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a9/
LA  - ru
ID  - VMUMM_2023_6_a9
ER  - 
%0 Journal Article
%A A. V. Aksenov
%T Equivalence of systems of two-dimensional shallow water equations over horizontal and sloping bottoms
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 62-64
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a9/
%G ru
%F VMUMM_2023_6_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

A point transformation determining the equivalence of systems of equations of two-dimensional shallow water over horizontal and sloping bottoms is obtained. The symmetries of these systems of equations are found.

[1] Stoker Dzh., Volny na vode. Matematicheskaya teoriya i prilozheniya, GIIL, M., 1959

[2] Ovsyannikov L.V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[3] Carrier G.F., Greenspan H.P., “Water waves of finite amplitude on a sloping beach”, J. Fluid Mech., 4:1 (1958), 97–109 | DOI | MR | Zbl

[4] Tuck E., Hwang L., “Long wave generation on a sloping beach”, J. Fluid Mech., 51:3 (1972), 449–461 | DOI | Zbl

[5] Pelinovsky E.N., Mazova R.Kh., “Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles”, Natural Hazards, 6:3 (1992), 227–249 | DOI

[6] Dobrokhotov S.Yu., Tirotstsi B., “Lokalizovannye resheniya odnomernoi nelineinoi sistemy uravnenii melkoi vody so skorostyu $c=\sqrt{x}$”, Uspekhi matem. nauk, 65:1 (2010), 185–186 | DOI | MR | Zbl