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

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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 $x$. 
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     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},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_3_a1/}
}
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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/