Geodesic
Perturbation theory for solitons in~the second approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 362-373

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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},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a6/}
}
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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/