Geodesic
Rapidly oscillating solutions of a generalized Korteweg–de Vries equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1812-1823 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a generalized Korteweg–de Vries equation, the existence of families of rapidly oscillating periodic solutions is proved and their asymptotic representation is found. The asymptotics of tori of different dimensions are examined. Formulas for solutions depending on all parameters of the problem are derived. 
@article{ZVMMF_2017_57_11_a5,
     author = {S. A. Kashchenko},
     title = {Rapidly oscillating solutions of a generalized {Korteweg{\textendash}de} {Vries} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1812--1823},
     year = {2017},
     volume = {57},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a5/}
}
TY  - JOUR
AU  - S. A. Kashchenko
TI  - Rapidly oscillating solutions of a generalized Korteweg–de Vries equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1812
EP  - 1823
VL  - 57
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a5/
LA  - ru
ID  - ZVMMF_2017_57_11_a5
ER  - 
%0 Journal Article
%A S. A. Kashchenko
%T Rapidly oscillating solutions of a generalized Korteweg–de Vries equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1812-1823
%V 57
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a5/
%G ru
%F ZVMMF_2017_57_11_a5
S. A. Kashchenko. Rapidly oscillating solutions of a generalized Korteweg–de Vries equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1812-1823. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a5/

[1] Korteweg D. J., de Vries G., “On the change of form of long waves advancing in a rectangular canal and on a new tipe of long stationary waves”, Phil. Mag., 39 (1895), 422–443 | DOI | MR

[2] Kudryashov N. A., Metody nelineinoi matematicheskoi fiziki, Uch. posobie, Izdatelskii Dom “Intellekt”, Dolgoprudnyi, 2010, 368 pp.

[3] Kudryashov N. A., “On “new travelling wave solutions” of the KdV and the KdV-Burgers equations”, Commun. Nonlinear Sci. Numer. Simul., 14:5 (2009), 1891–1900 | DOI | MR

[4] Kaschenko I. S., Kaschenko S. A., “Lokalnaya dinamika sistem raznostnykh i differentsialno-raznostnykh uravnenii”, Izv. vuzov “Prikladnaya nelineinaya dinamika”, 22:1 (2014), 71–92 | MR

[5] Kaschenko S. A., “O kvazinormalnykh formakh dlya parabolicheskikh uravnenii s maloi diffuziei”, Dokl. AN SSSR, 299:5 (1988), 1049–1053

[6] Kaschenko S. A., “Normalization in the systems with small diffusion”, Int. J. of Bifurcations and chaos, 6:7 (1996), 1093–1109 | DOI | MR

[7] Kaschenko I. S., Kaschenko S. A., “Kvazinormalnye formy dvukhkomponentnykh singulyarno vozmuschennykh sistem”, Dokl. AN, 447:4 (2012), 376–381 | MR

[8] Kaschenko I. S., “Multistabilnost v nelineinykh parabolicheskikh sistemakh s maloi diffuziei”, Dokl. AN, 435:2 (2010), 164–167 | MR

[9] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie sistemy i bifurkatsii vektornykh polei, In-t kompyuternykh issledovanii, M.–Izhevsk, 2002