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Mat. Sb., 1996, Volume 187, Number 5, Pages 71–110 (Mi msb129)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotic behaviour as $t\to \infty$ of the solutions of the generalized Korteweg–de Vries equation

P. I. Naumkin, I. A. Shishmarev

M. V. Lomonosov Moscow State University

Abstract: Asymptotic formulae representing for large time the solution of the Cauchy problem are obtained for the generalized Korteweg–de Vries equation with non-linear term to an integer power greater than three. The error terms are estimated. The method is based on the perturbation theory with respect to a parameter characterizing the smallness of the initial data.

DOI: https://doi.org/10.4213/sm129

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English version:
Sbornik: Mathematics, 1996, 187:5, 693–733

Bibliographic databases:

UDC: 517.9+535.5
MSC: 35Q20, 35B40
Received: 12.07.1994

Citation: P. I. Naumkin, I. A. Shishmarev, “Asymptotic behaviour as $t\to \infty$ of the solutions of the generalized Korteweg–de Vries equation”, Mat. Sb., 187:5 (1996), 71–110; Sb. Math., 187:5 (1996), 693–733

Citation in format AMSBIB
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\paper Asymptotic behaviour as $t\to \infty$ of the~solutions of the~generalized Korteweg--de~Vries equation
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\yr 1996
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\issue 5
\pages 71--110
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hayashi, N, “Large time asymptotics of solutions to the generalized Korteweg-de Vries equation”, Journal of Functional Analysis, 159:1 (1998), 110  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Hayashi, N, “Large time behavior of solutions for the modified Korteweg-de Vries equation”, International Mathematics Research Notices, 1999, no. 8, 395  crossref  mathscinet  zmath  isi  elib
    3. Hayashi N., Naumkin P., “On the modified Korteweg de Vries equation”, International Seminar Day on Diffraction, Proceedings, 1999, 146–156  crossref  isi  scopus  scopus  scopus
    4. Hayashi N. Naumkin P., “On the Modified Korteweg-de Vries Equation”, Math. Phys. Anal. Geom., 4:3 (2001), 197–227  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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