Geodesic
Perturbation theory for solitons in the second approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 362-373
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Equations for parameters of perturbed solitons which involve the terms up to the second order of smallness are obtained with the help of the perturbation theory for nonlinear waves based on the inverse scattering problem method. It is shown that for a sufficiently large class of perturbations these equations do not include secular terms. The procedure of obtaining the higher approximations is formulated. Examples of practical interest are considered. 
@article{TMF_1980_42_3_a6,
     author = {E. M. Maslov},
     title = {Perturbation theory for solitons in~the second approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {362--373},
     year = {1980},
     volume = {42},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a6/}
}
TY  - JOUR
AU  - E. M. Maslov
TI  - Perturbation theory for solitons in the second approximation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 362
EP  - 373
VL  - 42
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a6/
LA  - ru
ID  - TMF_1980_42_3_a6
ER  - 
%0 Journal Article
%A E. M. Maslov
%T Perturbation theory for solitons in the second approximation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 362-373
%V 42
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a6/
%G ru
%F TMF_1980_42_3_a6
E. M. Maslov. Perturbation theory for solitons in the second approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 362-373. http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a6/

[1] D. J. Kaup, SIAM J. Appl. Math., 31 (1976), 121 | DOI | MR | Zbl

[2] V. I. Karpman, E. M. Maslov, Preprint IZMIRAN No 1 (175), Moskva, 1977

[3] V. I. Karpman, E. M. Maslov, Phys. Lett., 60A (1977), 307 | DOI | MR

[4] V. I. Karpman, E. M. Maslov, Phys. Lett., 61A (1977), 355 ; 66A (1978), 513 | DOI | MR | MR

[5] V. I. Karpman, E. M. Maslov, ZhETF, 73 (1977), 537 ; 74 (1978), 1566 | MR | MR

[6] J. P. Keener, D. W. McLaughlin, Phys. Rev., 16A (1977), 777 | DOI | MR

[7] C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, Phys. Rev. Lett., 19 (1967), 1095 | DOI

[8] V. E. Zakharov, A. B. Shabat, ZhETF, 61 (1971), 118

[9] M. Wadati, J. Phys. Soc. Japan, 34 (1973), 1289 | DOI | MR | Zbl

[10] M. J. Ablowitz, D. J. Kaup, A. C. Newell, H. Segur, Phys. Rev. Lett., 31 (1973), 125 | DOI | MR | Zbl

[11] N. M. Krylov, N. N. Bogolyubov, Vvedenie v nelineinuyu mekhaniku, izd-vo AN USSR, 1937

[12] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, «Nauka», 1974 | MR

[13] V. I. Karpman, E. M. Maslov, ZhETF, 75 (1978), 504

[14] V. I. Karpman, E. M. Maslov, DAN SSSR, 242 (1978), 581 | MR