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 TMF, 1999, Volume 118, Number 3, Pages 434–440 (Mi tmf716)

Perturbation of a two-soliton solution of the Korteweg–de Vries equation in the case of close amplitudes

V. A. Lazarev

Ufa State University of Oil and Technology

Abstract: We investigate the interaction process for two solitons with close amplitudes under a small perturbation. The leading term of the formal asymptotic solution is found as the sum of two solitons with slowly varying parameters. The equations of slow variations are derived for the soliton phase shifts. The effects related to the interaction between the perturbed solitons can compensate the velocity difference in some conditions, which can result in the formation of the so-called quasi-stationary soliton pair.

DOI: https://doi.org/10.4213/tmf716

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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 341–346

Bibliographic databases:

Citation: V. A. Lazarev, “Perturbation of a two-soliton solution of the Korteweg–de Vries equation in the case of close amplitudes”, TMF, 118:3 (1999), 434–440; Theoret. and Math. Phys., 118:3 (1999), 341–346

Citation in format AMSBIB
\Bibitem{Laz99} \by V.~A.~Lazarev \paper Perturbation of a two-soliton solution of the Korteweg--de~Vries equation in the case of close amplitudes \jour TMF \yr 1999 \vol 118 \issue 3 \pages 434--440 \mathnet{http://mi.mathnet.ru/tmf716} \crossref{https://doi.org/10.4213/tmf716} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1713734} \zmath{https://zbmath.org/?q=an:0944.35086} \transl \jour Theoret. and Math. Phys. \yr 1999 \vol 118 \issue 3 \pages 341--346 \crossref{https://doi.org/10.1007/BF02557331} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000080492800014}