Geodesic
Asymptotic solitons of the sine-Gordon equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 15-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The large time asymptotics of the solutions of the sine-Gordon equation which tend to zero when $x\to\infty$ and tend to the finite-gap solution of this equation when $x\to-\infty$ are investigated. It is proved that at $t\to\infty$ these solutions split into infinite series of solitons with variable phases. These solitons are generated by the continuous spectrum of the $L$-operator from the corresponding Lax representation. 
@article{TMF_1989_80_1_a1,
     author = {V. P. Kotlyarov},
     title = {Asymptotic solitons of~the {sine-Gordon} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {15--28},
     year = {1989},
     volume = {80},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/}
}
TY  - JOUR
AU  - V. P. Kotlyarov
TI  - Asymptotic solitons of the sine-Gordon equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1989
SP  - 15
EP  - 28
VL  - 80
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/
LA  - ru
ID  - TMF_1989_80_1_a1
ER  - 
%0 Journal Article
%A V. P. Kotlyarov
%T Asymptotic solitons of the sine-Gordon equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1989
%P 15-28
%V 80
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/
%G ru
%F TMF_1989_80_1_a1
V. P. Kotlyarov. Asymptotic solitons of the sine-Gordon equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 1, pp. 15-28. http://geodesic.mathdoc.fr/item/TMF_1989_80_1_a1/

[1] Gurevich A. V., Pitaevskii L. P., ZhETF, 65:2 (1973), 590–604 | MR

[2] Khruslov E. Ya., Pisma v ZhETF, 21:8 (1975), 469–472 ; Мат. сб., 99:2 (1976), 261–281 | MR | MR | Zbl

[3] Ermakova V. D., DAN SSSR, ser. A, 1982, no. 7, 3–6 | MR | Zbl

[4] Kotlyarov V. P., Khruslov E. Ya., TMF, 68:2 (1986), 172–186 | MR | Zbl

[5] Kozel V. A., Kotlyarov V. P., DAN USSR, ser. A, 1976, no. 10, 878–881 ; Дифференциальные уравнения и некоторые методы функционального анализа, Сб. научн. трудов, Наукова думка, К., 1978, 89–103 | MR | Zbl

[6] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: metod obratnoi zadachi, Nauka, M., 1980 | MR

[7] Matveev V. B., Abelian functions and solitons, Preprint 373, University, Wroclaw, 1976

[8] Its A. R., Metod izomonodromnykh deformatsii v teorii vpolne integriruemykh nelineinykh evolyutsionnykh sistem, Dis. ...dokt. fiz.-mat. nauk, LGU, L., 1986

[9] Krichever I. M., “Nelineinye uravneniya i ellipticheskie krivye”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, VINITI, M., 1983, 79–136 | MR

[10] Kotlyarov V. P., Khruslov E. Ya., Asimptoticheskie solitony modifitsirovannogo uravneniya Kortevega-de Friza, Preprint 24-86, FTINT AN USSR, Kharkov, 1986

[11] Fedoryuk M. V., Metod perevala, Nauka, M., 1977 | MR

[12] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl