Geodesic
Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 281-299

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We present the approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). A series of assumptions about the form of solution and effects of Earth‘s rotation and bottom friction are made. Then the resulting ODE systems are solved. The corresponding free surfaces have first or second order. The conditions of finiteness and localization of a flow are analyzed. The solutions are used in the verification of numerical algorithm of the large particles method, the efficiency of the carried out tests is discussed. 
@article{SJVM_2019_22_3_a2,
     author = {N. A. Matskevich and L. B. Chubarov},
     title = {Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {281--299},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_3_a2/}
}
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N. A. Matskevich; L. B. Chubarov. Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 281-299. http://geodesic.mathdoc.fr/item/SJVM_2019_22_3_a2/