Geodesic
On a system of equations describing surface waves
Izvestiya. Mathematics, Tome 37 (1991) no. 1, pp. 119-156 
P. I. Naumkin; I. A. Shishmarev. On a system of equations describing surface waves. Izvestiya. Mathematics, Tome 37 (1991) no. 1, pp. 119-156. http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a5/
@article{IM2_1991_37_1_a5,
     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {On a system of equations describing surface waves},
     journal = {Izvestiya. Mathematics},
     pages = {119--156},
     year = {1991},
     volume = {37},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a5/}
}
TY  - JOUR
AU  - P. I. Naumkin
AU  - I. A. Shishmarev
TI  - On a system of equations describing surface waves
JO  - Izvestiya. Mathematics
PY  - 1991
SP  - 119
EP  - 156
VL  - 37
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a5/
LA  - en
ID  - IM2_1991_37_1_a5
ER  - 
%0 Journal Article
%A P. I. Naumkin
%A I. A. Shishmarev
%T On a system of equations describing surface waves
%J Izvestiya. Mathematics
%D 1991
%P 119-156
%V 37
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a5/
%G en
%F IM2_1991_37_1_a5

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

A new system of equations is proposed which describes surface waves in a fluid. The basic conservation laws are found for this system. The Cauchy problem for this system is considered, and the existence of a global solution (in time), the breakdown of a solution in finite time, and the smoothing of a discontinuous initial perturbation are studied.

[1] Uizem Dzh. B., Nelineinaya teoriya raspredeleniya voln, Mir, M., 1970

[2] Dobrokhotov S. Yu., “Nelokalnye analogi nelineinogo uravneniya Bussineska dlya poverkhnostnykh voln nad nerovnym dnom i ikh asimptoticheskie resheniya”, Dokl. AN SSSR, 292:1 (1987), 63–67 | MR | Zbl

[3] Uizem Dzh. B., Lineinye i nelineinye volny, Mir, M., 1977, 622 pp.

[4] Benjamin T. B., “Internal waves of permanent form in fluids of great depth”, J. Fluid. Mech., 29:3 (1967), 559 | DOI | MR | Zbl

[5] Ono H., “Algebraic solitary waves in stratified fluids”, J. Phys. Soc. Japan., 39:4 (1975), 1082 | DOI | MR

[6] Kadomtsev B. B., Petviashvili V. I., “Ob ustoichivosti uedinennykh voln v slabo dispergiruyuschikh sredakh”, Dokl. AN SSSR, 192 (1970), 753–755

[7] Zabolotskaya E. A., Khokhlov R. V., “Kvaziploskie volny v nelineinoi akustike otrazhennykh puchkov”, Akusticheskii zhurn., 15:1 (1969), 40–47

[8] Kaup D., “A higher-order water-waves equation and method for solving it”, Prog. Theor. Phys., 54 (1975), 396–408 | DOI | MR | Zbl

[9] Broer L., “Approximate equations for long water waves”, Appl. Sci. Res., 31 (1975), 377–395 | DOI | MR | Zbl