Geodesic
Perturbation of the Korteweg--de Vries soliton
Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 1, pp. 62-76

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For an arbitrary perturbation operator, equations for the modulation of the parameters of the KdV soiiton are obtained. The asymptotic behavior of the first correction is investigated, and the influence of the leading term of this asymptotic behavior on the soliton phase shift is demonstrated. 
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     author = {L. A. Kalyakin},
     title = {Perturbation of the {Korteweg--de} {Vries} soliton},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {92},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_92_1_a4/}
}
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L. A. Kalyakin. Perturbation of the Korteweg--de Vries soliton. Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 1, pp. 62-76. http://geodesic.mathdoc.fr/item/TMF_1992_92_1_a4/