Geodesic
A periodic problem for Whitham's equation
Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 403-426 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A periodic problem for the nonlinear and nonlocal Whitham equation is studied. Questions of the breakdown of a solution in finite time, the existence of a solution globally in time, and the smoothing of a discontinuous initial perturbation are considered. The asymptotics of a solution with respect to the smallness of the interaction is found. Bibliography: 10 titles. 
@article{SM_1990_67_2_a5,
     author = {P. I. Naumkin and I. A. Shishmarev},
     title = {A periodic problem for {Whitham's} equation},
     journal = {Sbornik. Mathematics},
     pages = {403--426},
     year = {1990},
     volume = {67},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/}
}
TY  - JOUR
AU  - P. I. Naumkin
AU  - I. A. Shishmarev
TI  - A periodic problem for Whitham's equation
JO  - Sbornik. Mathematics
PY  - 1990
SP  - 403
EP  - 426
VL  - 67
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/
LA  - en
ID  - SM_1990_67_2_a5
ER  - 
%0 Journal Article
%A P. I. Naumkin
%A I. A. Shishmarev
%T A periodic problem for Whitham's equation
%J Sbornik. Mathematics
%D 1990
%P 403-426
%V 67
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/
%G en
%F SM_1990_67_2_a5
P. I. Naumkin; I. A. Shishmarev. A periodic problem for Whitham's equation. Sbornik. Mathematics, Tome 67 (1990) no. 2, pp. 403-426. http://geodesic.mathdoc.fr/item/SM_1990_67_2_a5/

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

[2] Uizem Dzh. B., Lineinye i nelineinye volny, Mir, M., 1977 | MR

[3] Klimontovich Yu. L., Statisticheskaya teoriya neravnovesnykh protsessov v plazme, Izd-vo MGU, M., 1964

[4] Benjamin T. B., “Integral waves of permanent form in fluids of great depth”, J. Fluid Mech., 29:3 (1967), 559–592 | DOI | MR | Zbl

[5] Gabov S. A., “Ob uravnenii Uizema”, DAN SSSR, 242:5 (1978), 993–996 | MR | Zbl

[6] Naumkin P. I., Shishmarev I. A., “O suschestvovanii i razrushenii voln, opisyvaemykh uravneniem Uizema”, DAN SSSR, 288:1 (1986), 90–95 | MR | Zbl

[7] Naumkin P. I., Shishmarev I. A., “Oprokidyvanie voln dlya uravneniya Uizema s singulyarnym yadrom. II”, Differents. uravneniya, 21:10 (1985), 1775–1790 | MR | Zbl

[8] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | MR | Zbl

[9] Ono H., “Algebraic solitary waves in stratified fluids”, J. Phys. Soc. Japan, 39:4 (1975), 1082–1091 | DOI | MR

[10] Joseph R. I., “Multi-soliton-like solutions to the Benjamin–Ono equation”, J. Math. Phys., 18:12 (1977), 2251–2258 | DOI | MR | Zbl