Geodesic
Features of the dynamics of nonlinear waves in plane domains
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 628-645 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An analysis of the dynamics of three-dimensional nonlinear waves on a torus has shown that their attractors are the so-called self-organization regimes, which are created from trajectories crowding together and have several remarkable features. Specifically, they are well ordered with respect to spatial and time variables, and their energy is fairly high and decreases gradually with decreasing elasticity coefficient, which itself evolves into a diffusion chaos. The role of this paper is twofold. First, the features of self-organization regimes are analyzed in the case of Neumann boundary conditions. Second, the stages leading to the detection of this phenomenon are described in detail. 
@article{ZVMMF_2009_49_4_a5,
     author = {Yu. S. Kolesov and A. E. Khar'kov},
     title = {Features of the dynamics of nonlinear waves in plane domains},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {628--645},
     year = {2009},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a5/}
}
TY  - JOUR
AU  - Yu. S. Kolesov
AU  - A. E. Khar'kov
TI  - Features of the dynamics of nonlinear waves in plane domains
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 628
EP  - 645
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a5/
LA  - ru
ID  - ZVMMF_2009_49_4_a5
ER  - 
%0 Journal Article
%A Yu. S. Kolesov
%A A. E. Khar'kov
%T Features of the dynamics of nonlinear waves in plane domains
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 628-645
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a5/
%G ru
%F ZVMMF_2009_49_4_a5
Yu. S. Kolesov; A. E. Khar'kov. Features of the dynamics of nonlinear waves in plane domains. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 628-645. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a5/

[1] Kolesov Yu. S., Kharkov A. E., “Skhodstvo i razlichie dinamiki ploskikh i trekhmernykh nelineinykh voln”, Matem. sb., 196:2 (2005), 57–84 | MR | Zbl

[2] M. N. Mikhlin (red.), Lineinye uravneniya matematicheskoi fiziki, Nauka, M., 1964 | MR

[3] Kolesov Yu. S., “Asimptotika i ustoichivost nelineinykh parametricheskikh kolebanii singulyarno vozmuschennogo telegrafnogo uravneniya”, Matem. sb., 186:10 (1995), 57–72 | MR | Zbl

[4] Kolesov Yu. S., “Problema attraktorov nelineinykh volnovykh uravnenii v ploskikh oblastyakh”, Matem. zametki, 68:2 (2000), 217–229 | MR | Zbl

[5] Kolesov Yu. S., “Svoistva ustoichivosti tsiklov i torov prosteishego nerezonansnogo uravneniya volnovogo tipa”, Matem. zametki, 62:5 (1997), 744–750 | MR | Zbl

[6] Kolesov Yu. S., “Zadacha parazit-khozyain”, Dinamika biologicheskikh populyatsii, Izd-vo GGU, Gorkii, 1984, 16–29

[7] Kolesov Yu. S., “Ustoichivost i bifurkatsiya beguschikh voln”, Nelineinye kolebaniya v zadachakh ekologii, Izd-vo YarGU, Yaroslavl, 1985, 3–22 | MR

[8] Vainberg M. M., Trenogin B. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969 | MR | Zbl

[9] Mischenko E. F., Kolesov Yu. S., Kolesov A. Yu., Rozov N. Kh., Periodicheskie dvizheniya i bifurkatsionnye protsessy v singulyarno vozmuschennykh sistemakh, Fizmatlit, M., 1995 | MR

[10] Kolesov Yu. S., Maiorov V. V., “Prostranstvennaya i vremennaya samoorganizatsiya v odnovidovom biotsenoze”, Dinamika biologicheskikh populyatsii, Izd-vo GGU, Gorkii, 1986, 3–18