Geodesic
Special classes of solutions to the equations of horizontal-displacement fluid motion
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 3, pp. 50-57 
P. V. Kovtunenko; A. A. Chesnokov. Special classes of solutions to the equations of horizontal-displacement fluid motion. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 3, pp. 50-57. http://geodesic.mathdoc.fr/item/SJIM_2011_14_3_a5/
@article{SJIM_2011_14_3_a5,
     author = {P. V. Kovtunenko and A. A. Chesnokov},
     title = {Special classes of solutions to the equations of horizontal-displacement fluid motion},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {50--57},
     year = {2011},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_3_a5/}
}
TY  - JOUR
AU  - P. V. Kovtunenko
AU  - A. A. Chesnokov
TI  - Special classes of solutions to the equations of horizontal-displacement fluid motion
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2011
SP  - 50
EP  - 57
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2011_14_3_a5/
LA  - ru
ID  - SJIM_2011_14_3_a5
ER  - 
%0 Journal Article
%A P. V. Kovtunenko
%A A. A. Chesnokov
%T Special classes of solutions to the equations of horizontal-displacement fluid motion
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2011
%P 50-57
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2011_14_3_a5/
%G ru
%F SJIM_2011_14_3_a5

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

We construct a special class of solutions to nonlinear integrodifferential equations describing horizontal-displacement motion of ideal fluid in an open channel in the shallow water approximation. This class of solutions is characterized by a linear relation among Riemann integral invariants and is determined by a hyperbolic system of two differential equations with two parameters. In the class of traveling waves we construct exact solutions, including arbitrary functions, to the equations of motion continuously adjacent to a given displacement flow.

[1] Chesnokov A. A., Lyapidevskii V. Yu., “Volnovye dvizheniya idealnoi zhidkosti v uzkom otkrytom kanale”, Prikl. mekhanika i tekhn. fizika, 50:2 (2009), 61–71 | MR

[2] Lyapidevskii V. Yu., Chesnokov A. A., “Dokriticheskie i sverkhkriticheskie gorizontalno- sdvigovye techeniya v otkrytom kanale peremennogo secheniya”, Izv. RAN. Mekhanika zhidkosti i gaza, 2009, no. 6, 123–138

[3] Teshukov V. M., “O giperbolichnosti uravnenii dlinnykh voln”, Dokl. AN SSSR, 284:3 (1985), 555–559 | MR | Zbl

[4] Vlasov A. A., Teoriya mnogikh chastits, Gostekhizdat, M.–L., 1950

[5] Teshukov V., Russo G., Chesnokov A., “Analytical and numerical solutions of the shallow water equations for 2-D rotational flows”, Math. Models Methods Appl. Sci., 14 (2004), 1451–1479 | DOI | MR | Zbl

[6] Benney D. J., “Some properties of long nonlinear waves”, Stud. Appl. Math., 52 (1973), 45–50 | Zbl

[7] Lyapidevskii V. Yu., Teshukov V. M., Matematicheskie modeli rasprostraneniya dlinnykh voln v neodnorodnoi zhidkosti, Izd-vo SO RAN, Novosibirsk, 2000

[8] Teshukov V. M., “Kharakteristiki, zakony sokhraneniya i simmetrii kineticheskikh uravnenii dvizheniya puzyrkov v zhidkosti”, Prikl. mekhanika i tekhn. fizika, 40:2 (1999), 86–100 | MR | Zbl

[9] Drazin F., Vvedenie v teoriyu gidrodinamicheskoi ustoichivosti, Fizmatlit, M., 2005