Geodesic
Solitons of the Korteweg-de Vries equation on the background of a known solution
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 333-339 
A. V. Rybin; M. A. Sall'. Solitons of the Korteweg-de Vries equation on the background of a known solution. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 3, pp. 333-339. http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a1/
@article{TMF_1985_63_3_a1,
     author = {A. V. Rybin and M. A. Sall'},
     title = {Solitons of the {Korteweg-de~Vries} equation on the background of a~known solution},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {333--339},
     year = {1985},
     volume = {63},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a1/}
}
TY  - JOUR
AU  - A. V. Rybin
AU  - M. A. Sall'
TI  - Solitons of the Korteweg-de Vries equation on the background of a known solution
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1985
SP  - 333
EP  - 339
VL  - 63
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a1/
LA  - ru
ID  - TMF_1985_63_3_a1
ER  - 
%0 Journal Article
%A A. V. Rybin
%A M. A. Sall'
%T Solitons of the Korteweg-de Vries equation on the background of a known solution
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1985
%P 333-339
%V 63
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a1/
%G ru
%F TMF_1985_63_3_a1

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

Asymptotic expressions describing the propagation of solitons on the background of an arbitrary solution are obtained. A study is made of the problem of finding the phase shifts of such solitons when they interact in pairs and also when a soliton interacts with a solution that decreases with respect to $x$.

[1] Matveev V. B., Lett. Math. Phys., 3 (1979), 213–216 | DOI | MR | Zbl

[2] Matveev V. B., Lett. Math. Phys., 3 (1979), 217–222 | DOI | MR | Zbl

[3] Bobenko A. I., Matveev V. B., Sall M. A., DAN SSSR, 265:6 (1982), 1357–1360 | MR | Zbl

[4] Matveev V. B., Sall M. A., Zap. nauchn. semin. LOMI, 120, 1982, 96–101 | MR

[5] Sall M. A., TMF, 53:2 (1982), 227–237 | MR | Zbl

[6] Bobenko A. I., Vestn. LGU, 1982, no. 4, 14–21 | MR

[7] Wahlquist H., Lect. Notes in Math., 515, 1974, 103–145

[8] Karpman V. I., Maslov E. M., O vozmuscheniyakh, sokhranyayuschikh solitony, Preprint IZMIRAN, No 51 (259), IZMIRAN, M., 1979

[9] Maslov E. M., K teorii vozmuschenii dlya solitonov vo vtorom priblizhenii, Preprint IZMIRAN, No 5 (234), IZMIRAN, M., 1979 | MR

[10] P. Uslengi (red.), Nelineinye elektromagnitnye volny, Mir, M., 1983

[11] Wadati M., J. Phys. Soc. Yapan, 52:8 (1983) | MR

[12] Miura R. M., Gardner C. S., Kruskal M. D., J. Math. Phys., 9 (1968), 1204–1209 | DOI | MR | Zbl