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Mat. Sb., 1995, Volume 186, Number 7, Pages 51–76 (Mi msb53)  

This article is cited in 2 scientific papers (total in 2 papers)

On the problem of first correction in soliton perturbation theory

L. A. Kalyakin

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

Abstract: For an integro-differential equation with rapidly oscillating kernel of Cauchy type it is proved that a solution exists and is uniformly bounded in the Holder norm with respect to a small parameter $\varepsilon$. This equation describes the essential part of the first correction in soliton perturbation theory. An asymptotic estimate is obtained for this correction, which implies that the soliton structure of the solution of an equation close to the integral equation is preserved for times $\sim\varepsilon^{-1}$.

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English version:
Sbornik: Mathematics, 1995, 186:7, 977–1002

Bibliographic databases:

UDC: 517.956.226
MSC: Primary 35Q51; Secondary 35B20
Received: 11.03.1992 and 10.03.1993

Citation: L. A. Kalyakin, “On the problem of first correction in soliton perturbation theory”, Mat. Sb., 186:7 (1995), 51–76; Sb. Math., 186:7 (1995), 977–1002

Citation in format AMSBIB
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\by L.~A.~Kalyakin
\paper On the problem of first correction in soliton perturbation theory
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 7
\pages 51--76
\mathnet{http://mi.mathnet.ru/msb53}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1355456}
\zmath{https://zbmath.org/?q=an:0863.35092}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 7
\pages 977--1002
\crossref{https://doi.org/10.1070/SM1995v186n07ABEH000053}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TX11200005}


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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. Kalyakin L., “Asymptotic Well-Posedness for the Problem of Soliton Perturbation”, Russ. J. Math. Phys., 5:4 (1997), 447–458  mathscinet  zmath  isi
    2. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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