Geodesic
Asymptotic expansions and qualitative analysis of finite-dimensional models in nonlinear field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 395-403 
V. M. Eleonskii; N. E. Kulagin; N. S. Novozhilova; V. P. Silin. Asymptotic expansions and qualitative analysis of finite-dimensional models in nonlinear field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 395-403. http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a5/
@article{TMF_1984_60_3_a5,
     author = {V. M. Eleonskii and N. E. Kulagin and N. S. Novozhilova and V. P. Silin},
     title = {Asymptotic expansions and qualitative analysis of finite-dimensional models in nonlinear field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {395--403},
     year = {1984},
     volume = {60},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a5/}
}
TY  - JOUR
AU  - V. M. Eleonskii
AU  - N. E. Kulagin
AU  - N. S. Novozhilova
AU  - V. P. Silin
TI  - Asymptotic expansions and qualitative analysis of finite-dimensional models in nonlinear field theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 395
EP  - 403
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a5/
LA  - ru
ID  - TMF_1984_60_3_a5
ER  - 
%0 Journal Article
%A V. M. Eleonskii
%A N. E. Kulagin
%A N. S. Novozhilova
%A V. P. Silin
%T Asymptotic expansions and qualitative analysis of finite-dimensional models in nonlinear field theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 395-403
%V 60
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a5/
%G ru
%F TMF_1984_60_3_a5

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

The methods of the qualitative theory of dynamical systems are used to establish the reasons that prevent the nonlinear wave equation $\square u =F(u)$ from having solutions that are periodic in time and self-localized in space. The correspondence between the qualitative behavior of the singular (separatrix) trajectories in the phase space and the asymptotic solutions of the nonlinear wave equation is considered.

[1] Bogolyubov N. N., Izbrannye trudy, t. I, Naukova dumka, Kiev, 1971, 257–337 | MR

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

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

[4] Eleonskii V. M., Silin V. P., ZhETF, 56 (1969), 574–591; 57, 478–488

[5] Kosevich A. M., Kovalev A. S., ZhETF, 67 (1974), 1793–1804

[6] Dashen R., Hasslasher B., Neven A., Phys. Rev. D, 11:12 (1975), 3424–3449 | DOI | MR

[7] Voronov N. A., Kobzarev I. Yu., Pisma v ZhETF, 24 (1976), 576–579

[8] Makhankov V. G., Phys. Rep., 35:1 (1978), 1–128 | DOI | MR

[9] Buslaev V. S., TMF, 31:1 (1977), 23–32 | MR | Zbl

[10] Eleonskii V. M., Kulagin N. E., Novozhilova N. S., Silin V. P., Kratkie soobscheniya po fizike FIAN, 1981, no. 4, 47–51

[11] Segyr H., J. Math. Phys., 24:6 (1983), 1439–1443 | DOI | MR

[12] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974, 362 pp. | MR

[13] Eleonskii V. M., Kulagin N. E., Novozhilova N. S., Silin V. P., “O samolokalizovannykh v prostranstve i periodicheskikh vo vremeni resheniyakh volnovykh uravnenii”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. sb., Gos. un-t, Gorkii, 1982, 73–92 | MR

[14] Eleonskii V. M., Kulagin N. E., Novozhilova N. S., Silin V. P., Metod Bogolyubova - Mitropolskogo i metod Tamma - Dankova v teorii nelineinogo polya, Preprint FIAN, No 279, FIAN SSSR, Moskva, 1982 | MR

[15] S. P. Novikov (red.), Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR