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 Mat. Zametki, 1995, Volume 58, Issue 2, Pages 204–217 (Mi mz2037)

Asymptotics of the first correction in the perturbation of the $N$-soliton solution to the KdV equation

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: We consider a triple Fourier-type integral that represents a solution to the KdV equation linearized on an $N$-soliton potential. Assuming that the parameters of the potential depend on the slow time $t$, we construct an asymptotics of this integral as $\varepsilon\to0$ uniform with respect to $x$, $t$ up to large time $0<t\le O(\varepsilon^{-1})$.

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English version:
Mathematical Notes, 1995, 58:2, 814–823

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Citation: L. A. Kalyakin, “Asymptotics of the first correction in the perturbation of the $N$-soliton solution to the KdV equation”, Mat. Zametki, 58:2 (1995), 204–217; Math. Notes, 58:2 (1995), 814–823

Citation in format AMSBIB
\Bibitem{Kal95} \by L.~A.~Kalyakin \paper Asymptotics of the first correction in the perturbation of the $N$-soliton solution to the KdV equation \jour Mat. Zametki \yr 1995 \vol 58 \issue 2 \pages 204--217 \mathnet{http://mi.mathnet.ru/mz2037} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1367219} \zmath{https://zbmath.org/?q=an:0849.35120} \transl \jour Math. Notes \yr 1995 \vol 58 \issue 2 \pages 814--823 \crossref{https://doi.org/10.1007/BF02304103} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TV39900018} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. A. Kalyakin, V. A. Lazarev, “Perturbation of the two-soliton solution of the KdV equation”, Theoret. and Math. Phys., 112:1 (1997), 866–874
2. V. A. Lazarev, “Perturbation of a two-soliton solution of the Korteweg–de Vries equation in the case of close amplitudes”, Theoret. and Math. Phys., 118:3 (1999), 341–346
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