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
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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.
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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/

[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