Geodesic
Existence of countably many stable cycles in media with dispersion
Izvestiya. Mathematics, Tome 59 (1995) no. 3, pp. 579-595 
A. Yu. Kolesov. Existence of countably many stable cycles in media with dispersion. Izvestiya. Mathematics, Tome 59 (1995) no. 3, pp. 579-595. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a4/
@article{IM2_1995_59_3_a4,
     author = {A. Yu. Kolesov},
     title = {Existence of countably many stable cycles in media with dispersion},
     journal = {Izvestiya. Mathematics},
     pages = {579--595},
     year = {1995},
     volume = {59},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a4/}
}
TY  - JOUR
AU  - A. Yu. Kolesov
TI  - Existence of countably many stable cycles in media with dispersion
JO  - Izvestiya. Mathematics
PY  - 1995
SP  - 579
EP  - 595
VL  - 59
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a4/
LA  - en
ID  - IM2_1995_59_3_a4
ER  - 
%0 Journal Article
%A A. Yu. Kolesov
%T Existence of countably many stable cycles in media with dispersion
%J Izvestiya. Mathematics
%D 1995
%P 579-595
%V 59
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a4/
%G en
%F IM2_1995_59_3_a4

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

The problem in the title is analyzed in two typical examples of equations with dispersion: the Korteweg–de Vries equation, and the equation for vibrations of a beam. Also, features of the dynamics are considered for the Boussinesq equation, which does not have dispersion.

[1] Kolesov A. Yu., “Ustoichivost avtokolebanii telegrafnogo uravneniya, bifurtsiruyuschikh iz sostoyaniya ravnovesiya”, Matem. zametki, 51:2 (1992), 59–65 | MR | Zbl

[2] Nelineinye volny, eds. S. Leibovich, A. Sibass, Mir, M., 1977 | MR

[3] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[4] Kolesov Yu. S., Maiorov V. V., “Novyi metod issledovaniya ustoichivykh reshenii lineinykh differentsialnykh uravnenii s blizkimi k postoyannym pochti periodicheskimi koeffitsientami”, Differents. uravneniya, 10:10 (1974), 1778–1787 | MR

[5] Kolesov A. Yu., “Avtokolebaniya singulyarno vozmuschennykh parabolicheskikh sistem pervoi stepeni negrubosti”, Matem. zametki, 49:5 (1991), 62–69 | MR | Zbl